There is no clear origin for the term:

Big Blue is a nickname for IBM. There are several theories explaining the origin of the name. One theory, substantiated by people who worked for IBM at the time, is that IBM field representatives coined the term in the 1960s, referring to the color of the mainframes IBM installed in the 1960s and early 1970s. “All blue” was a term used to describe a loyal IBM customer, and business writers later picked up the term. Another theory suggests that Big Blue simply refers to the Company’s logo. A third theory suggests that Big Blue refers to a former company dress code that required many IBM employees to wear only white shirts and many wore blue suits. In any event, IBM keyboards, typewriters, and some other manufactured devices have played on the “Big Blue” concept, using the color for enter keys and carriage returns. (Source: IBM article, Wikipedia)

The nickname uses the negative sense of “black” indicating something secret, bad, or nefarious, as in “black market” or “black sites.” This usage of “black” stands in particular contrast to the “white” in the team’s real name.

The red tops include:

• The Daily Mirror
• The Daily Star
• The Sun

This nickname refers to the Three Branches of the United States Government which are provided for in the United States Constitution. The most common usages of this nickname are for:

The Federal Reserve System, the central bank of the country:

• “With the worst moments of the Great Panic apparently past, Mr. Bernanke finds himself celebrated by some as a hero. But he is accused by many others of pursuing bailouts that teach Wall Street gamblers that the Fed will save them from their own mistakes, of confusing markets by saving Bear Stearns and AIG but condemning Lehman, of meddling improperly by secretly pressuring Bank of America to stick to its planned purchase of Merrill Lynch — even of usurping the prerogatives of elected politicians. In the Great Panic, the Fed emerged as almost a fourth branch of government during the crisis, deciding which financial firms would live and which would die and lending hundreds of billions of dollars and putting taxpayers at risk without having to get congressional approval — to the surprise and consternation of some elected politicians. ‘It’s been inappropriate in a democracy,’ said Barney Frank, the Massachusetts Democrat. ‘There’s a terrible situation and you just hope that the chairman of the Federal Reserve would pop up with the secretary of the Treasury and rescue you.’”—David Wessel, “Financial Crisis: Inside Dr. Bernanke’s E.R.: As Obama considers reappointing the Fed chairman, a look at how he took on more power,” The Wall Street Journal, July 18, 2009.
• “The Federal Reserve Board has long been one of the rare institutions in our democracy—like the Supreme Court—whose internal processes are largely shielded from public view. Though not quite a fourth branch of government, the Fed’s independence is no less vital, in its own way, than that of the justices. There wouldn’t be much point in having a central bank if its every technical decision about the money supply were subject to short-term political debate. But the Fed’s unprecedented interventions in the economy during the current financial crisis have stirred challenges to this view. It’s uncontroversial to keep Fed decisions about setting interest rates and other traditional functions confidential — but details of the Fed’s unprecedented lending to particular companies such as Bear Stearns or AIG—or others yet unnamed—is a different matter. After all, the citizenry will reap the results of these commitments, which the Fed has made under its seldom-used — and very broad — emergency authorities. Under Chairman Ben S. Bernanke, the Fed has moved toward greater openness. Still, two-thirds of the House supports a bill sponsored by the Fed’s arch-nemesis, Ron Paul (R-Tex.), that would require annual audits of its monetary policymaking and short-term lending.”—unsigned editorial, “FOIA and the Fed: Do we have a right to know the central bank’s inner workings?” The Washington Post, October 22, 2009, p. A24.

The Press, which is more commonly nicknamed, “the Fourth Estate”:

• “Justice Stewart Potter may have said it best in 1975, when he wrote, ‘The primary purpose of the constitutional guarantee of a free press was to create a fourth institution outside the Government as an additional check on the three official branches.’ Clearly, the American press, as that essential ‘fourth branch of government,’ along with the judicial and public policy protections guiding it, constitutes one of the greatest achievements of the nation. But what the press will become in this new century is a matter of both uncertainty and utmost importance.”–Lee C. Bollinger, “Freedom of the press in the 21st century,” The New Orleans Times-Picayune, October 12, 2008.
• “That wisdom apparently doesn’t extend to Massachusetts Senator John Kerry, who held a hearing on the future of newspapers — and how the federal government can help. ‘If we take seriously this notion that the press is the fourth estate, or the fourth branch of government,’ Mr. Kerry said in a prepared statement, it’s time we consider its importance to democracy. Talk about a Freudian slip. Newspapers becoming the ‘fourth branch of government‘ is exactly what people most fear from any hand extended to save an independent press.”—unsigned editorial, “Ink-Stained Politicians,” The Wall Street Journal, May 16, 2009, p. A10.
• “Thomas Jefferson once wrote: ‘Were it left to me to decide whether we should have a government without newspapers or newspapers without a government, I should not hesitate a moment to prefer the latter.’ Looking at a modern newspaper landscape whipsawed by focus groups and quarterly earnings reports, I wonder whether he’d have said the same today. In Jefferson’s time, the press was often scurrilous but also vital. No one talked about newspapers as the fourth branch of government, a role too many of today’s elite journalists seem to take literally. Since journalism polished its veneer of professionalism in the last century, more reporters hold cum laude degrees. But far fewer live in the communities they cover. Perhaps it’s not too late for more of them to wander away from the halls of power onto the streets, away from those making policy pronouncements and toward those living under their weight.”—Jerry Lanson, “As the Globe reels, papers must drop elitism,” The Christian Science Monitor, June 9, 2009.

The Vice Presidency:

• “The vice presidency, a constitutional afterthought and for most of its history little more than a V.I.P. parking spot, has evolved tremendously since Nelson A. Rockefeller derided its occupant—for a brief unhappy time, himself—as ‘standby equipment.’ Three decades after Mr. Rockefeller departed the office, Dick Cheney has transformed it into a veritable fourth branch of government. Mr. Cheney pursued his agenda across a broad range of policy, including the war in Iraq, treatment of suspected terrorists, domestic surveillance, energy and the environment. His authority at times seemed to eclipse that of President Bush.”—John M. Broder, “The Heartbeat Job,” The New York Times, October 5, 2008.

The Department of the Treasury:

• “John Locke’s ‘Second Treatise of Civil Government’ (1690), which deeply influenced America’s Founders, says: ‘The legislative cannot transfer the power of making laws to any other hands: for it being but a delegated power from the people, they who have it cannot pass it over to others.’ And: ‘The power of the legislative … being only to make laws, and not to make legislators, the legislative can have no power to transfer their authority of making laws, and place it in other hands.’ But that is essentially what TARP has done. It has made Treasury Department bureaucrats into legislators; or perhaps it has made Secretary Hank Paulson the fourth branch of government.”—George F. Will, “TARP and ADD: Congress has made bureaucrats into legislators, or perhaps it has made Hank Paulson into the fourth branch of government,” Newsweek, December 1, 2008.

Lobbyists:

• “A John McCain-Barack Obama matchup will pit a pair of self- styled reformers in the race for president this fall, which explains why they are spending so much of the early rounds trying to outmuscle each other to prove who is tougher on this political season’s whipping boy, the Washington lobbyist. But lobbyists and many independent analysts view the candidates’ antilobbyist rhetoric as grandstanding to score political points at the expense of the vast, multibillion-dollar advocacy industry that is sometimes called the fourth branch of the United States government.”—Brian C. Mooney, “Lobbyists are boon as well as bane for McCain, Obama: Candidates’ criticisms seen as grandstanding,” The Boston Globe, June 1, 2008, p. A6.

• John Lennon
• Paul McCartney
• George Harrison
• Ringo Starr

The phrase has also become a general nickname for groups of four people, whether they are artists, sports figures, in an organized group or not:

• “Of course, London’s design establishment has long since perfected the tricky cocktail of originality and commercial nous. Experience has taught them vital lessons about their customers and, in the case of the fab four—Betty Jackson, Nicole Farhi, Dame Vivienne Westwood and Sir Paul Smith—they could provide a DNA profile of their loyal shoppers, they know them so well.”—Nicola Copping and Vanessa Friedman, “Cutting edge turns commercial,” The Financial Times, September 25, 2009
• “Collaborating with the Pulitzer Prize-winning journalist Buzz Bissinger, James tells the story of his tightknit bond with his friends from Akron, Ohio: Sian Cotton, Willie McGee and Dru Joyce III, known as Little Dru. They were a band of basketball brothers, playing together first on the Shooting Stars, an Amateur Athletic Union team, and then at St. Vincent-St. Mary High School. They called themselves the Fab Four and later, with the addition of Romeo Travis, the Fab Five. (A documentary film about James’s high school team, ‘More Than a Game,’ had its premiere at the Toronto International Film Festival last year and has just been released in theaters.)”—Ishan Taylor, “The King James Version,” The New York Times, October 4, 2009

It can also be used—less commonly—as a nickname for:

• Compost: “A household produces about a tonne of organic waste annually, she explains; wigglers eat half their weight daily, and in one year, a half kilo of them, numbering 800 to 1,000, and their offspring, can convert that tonne of material into ‘black gold.’”—Ellen Moorhouse, “Learning to love the magic of worms; Red wigglers can turn your garbage into ‘black gold’ so meet vermicomposting advocate Cathy Nesbitt,” The Toronto Star, September 19, 2009
• Bluefin Tuna: “Fishermen here call it ‘black gold,’ referring to the dark red flesh of the Pacific bluefin tuna that is so prized in this sashimi-loving nation that just one of these sleek fish, which can weigh a half-ton, can earn tens of thousands of dollars.”—Martin Fackler, “Tuna Town In Japan Sees Falloff Of Its Fish,” The New York Times, September 20, 2009
• Black Peppercorns: “If those vital downpours have not washed away what passes for the road, a few days travel into Kerala’s rolling Western Ghats, where waterfalls roar and herds of wild elephants loom from soft mist, brings you to the ancestral home of Piper nigrum.  High up in the middle of nowhere, Iddicki produces the finest pepper in the world, its peppercorns always dark and heavy, bursting with flavour.  Its vines wind their way around almost every tree in sight, climbing ten metres or more into the sky. After such a journey you might expect Iddicki to be a sleepy backwater.  In its own idyllic way, though, it is a boomtown worthy of the Wild West.  Fancy jeeps clog the narrow streets; shops overflow with the latest necessities of rural life, like washing machines and stereos.  Giant satellite dishes shove their expensive snouts at the heavens from every other house.  One of the world’s largest stashes of gold is in rural India, and to judge by its glittering jewellery shops this town has considerably more than its fair share.  ‘Black gold,’ explains one pepper farmer with a broad grin, is fetching top prices on the world market.”—No author, “The Spice Trade:  A taste of adventure; The history of spices is the history of trade,” The Economist, December 19, 1998, p. 51

During World War II, Mr. Gulbenkian settled Lisbon, Portugal where he died in 1955.  A large portion of his wealth was used to establish the Fundação Calouste Gulbenkian, which today has assets of around €2.5 billion and an annual budget of around €100 million.  In addition, his extensive collection of art, which included paintings by Rubens, Degas, and Monet, as well as ancient Egyptian sculptures and jewelery created by René Lalique, who was a personal friend, was used to create the Museu Calouste Gulbenkian in Lisbon.