The term third party is used in the United States for a political party other than one of the two major parties (Democratic Party and Republican Party). It can also include independents and write-in candidates.
The United States has had a two-party system for over a century. Following Duverger's law, the winner take all system for presidential elections and the single-seat plurality voting system for Congressional elections have over time created the two-party system.
Third party candidates very rarely win any elections. For example, such a candidate only won a U.S. Senate election twice (0.6%) since 1990. Therefore, it is very rare to have a national officeholder without having a party affiliation with a major party. Currently, there are only two U.S. Senators (Joe Lieberman and Bernie Sanders), who are neither Democrat nor Republican, while no U.S. Representative hails from outside the major parties. The only two U.S. Presidents without a major party affiliation were George Washington and Andrew Johnson. Andrew Johnson switched from Unionist to independent while in office. He had been elected with Lincoln under the "Union" banner in 1864, after serving as Democratic Senator and Governor in Tennessee. Currently Governor Lincoln Chafee, an Independent in Rhode Island, is the only one serving. There have been 20th Century governors elected as Independent, and from such parties as Progressive, Reform, Farmer-Labor, Populist, and Prohibition. There were others in the century before. Greens, Libertarians and others have elected state Legislators and local officials. The Socialists had 600 mayors at one time before World War I, including Milwaukee, New Haven, Reading Pa., and Schenectedy.
The odds are a third party will only serve to re-elect Obama.