The title says it all folks: Top Gun. The film was based on an article called "Top Guns" written by Ehud Yonay and published in California magazine in 1983. Paramount Pictures bought the rights to the article so they could make a movie out of the story and use the title (the article was about fighter pilots at Top Gun).
But that's not all there is to the story. While on the one hand the title of the film is simply the name of the elite fighter weapons school the pilots attend, it also describes one of the film's major questions: who is the top gun? Is it Maverick? Is it Iceman? Are they both the top guns? Is neither one the top gun?
By the end of the film it is clear that Maverick really is the top gun. He saves Iceman's life, and he saves the day. He may be impulsive, he may be unorthodox, but he's learned how to harness those forces to be the best in the Navy (or the best that we see).
In some ways the film is also about who the top gun is on a more global scale: the United States, or the unnamed communist country? The film suggests at the end that it is because of a school like Top Gun that the United States is the top gun when comes to aerial combat.