Big 4 usually refers to the four largest accounting and auditing firms: PricewaterhouseCoopers, Deloitte Touche Tohmatsu, Ernst & Young, and KPMG. These certified public accounting (CPA) firms perform most of the audits which are required of U.S. corporations having stock that is publicly traded.
In the 1980s and before, the majority of the audits of publicly traded corporations were performed by the Big 8—the eight largest CPA firms. However, some of those firms merged with others and Arthur Andersen ceased to exist. As a result, the Big 8 is now the Big 4.
The reference to Big 4 exists because the size of each of the four largest firms is several times the size of the 5th largest firm. There was a similar size disparity in the 1980s between the 8th largest firm and the 9th largest firm.
In addition to performing audits and other assurance services, the Big 4 provide tax advising and various management services.