Under U.S. tax law, there are two kinds of corporations: S corporations and C corporations. Section 1361(a)(2) of the Internal Revenue Code defines a C corporation as "with respect to any taxable year, a corporation which is not an S corporation for such year." A corporation must meet certain criteria and its shareholders must make a voluntary election to become an S corporation; if the corporation doesn't do both, it is treated as a C corporation.
The main difference between the two is that a C corporation must pay income tax on its own profits, and its shareholders must also pay income tax on dividends they receive from the corporation. An S corporation is not subject to this sort of double taxation; it pays no taxes as an entity. So most corporations that can become S corporations will choose to become S corporations; less money goes to The Man that way.
However, if a corporation falls under any of the following categories, it can't become an S corporation and therefore has to be a C corporation:
So most of the corporations you've heard of are probably C corporations.
The name comes from Subchapter C of the Internal Revenue Code, which covers corporate taxes. S corporations are, unsurprisingly, taxed under Subchapter S.