Without knowing precisely what period of American history you are referring to, it is a little hard to explain who the Big Four are. There were a few cadres who were called the Big Four;
The Big Four is a popular name given to the entrepreneurs who headed the Central Pacific Railroad. Their membership included Charles Crocker, Mark Hopkins, Collis Huntington and most famously Leland Stanford. Stanford is probably most well known for using his railroad money to build Stanford University in California. These men oversaw the building of the western portion of the transcontinental railroad, and became very wealthy as a result.
The Big Four could also refer to the four chief participants in the Paris Peace Conference which ended World War I in 1919. They were President Woodrow Wilson of the U.S., Prime Minister David Lloyd George of Great Britain, Vittorio Orlando of Italy and Prime Minister Georges Clemenceau of France. These men drafted a peace plan which was ultimately signed by twenty nations ending the war and creating the League of Nations. The U.S. failed to ratify this treaty, and slipped back into isolation despite Wilson’s best efforts.
Also, although I don’t think this is what you meant, The Big Four could mean the four debutants that ruled Chicago’s social scene in the early 1900’s. They were Ginevra King who dated F. Scott Fitzgerald, Edith Cummings the famous golfer , Courtney Letts who married the ambassador of Argentina and Margaret Carry who was famous by her association with the other three.