Words that sound alike but have different meanings or spellings are called homophones. A simple example of this would be the words dear and deer.
While everyone reading this is probably able to distinguish those two words, here is a tricky pair that often gets confused: premier and premiere.
These words come from the French word meaning "first," the only difference in French being the masculine (premier) and feminine (première) forms of the adjective.
In English, however, premier refers specifically to something that is first, best or most important. So if a violinist is first chair, it could be said that he/she is the premier violinist in an orchestra. The best mystery writer might be called a premier whodunnit author. The leader of a Canadian province (analogous to a U.S. governor) is called a Premier. The top league in English soccer is called the Premier League or simply the Premiership.
The other form, premiere, refers to the first performance, exhibition, screening, etc., of a piece of music, a play, a film or other work of art. It could also be a person's first performance or debut. Examples would be attending the premiere of Will Ferrell's film "Blades of Glory" or witnessing Osmo Vänskä's Minneapolis premiere.
It's conceivable that if there's an opening performance of something and it turns out to be the best one in recent memory, it could be said it was "the premier premiere of the year"... but that's not advisable.
Source: Oxford Dictionary of Current English, 2001.