1. As a quick shorthand for "opposition to homosexuality" or "the belief that homosexuality is sinful" and so on. The media prefer short words to cumbersome phrases, so the term prospered.
2. As a snarl word to imply that it's irrational or hateful to oppose homosexuality or to call it sinful. As such, it's an effective way to end debate on homosexuality. Simply call someone homophobic (meaning that they are irrational), and then it's obviously pointless to continue the discussion: who argues with crazy people or hatemongers?