Film music is any music used in films. There are many different styles, but film music scores can be distinguished first of all as composed or compiled. Composed scores tend to tell the viewer what emotions to feel. Compiled scores tend to evoke emotions through associations the viewer already has with the music.

History

In the early twentieth century, pianists accompanied films on the piano, improvising on stock musical phrases. Sound films at first only used composed scores (scores with music written for the film, typically orchestral). Starting in the late twentieth century, films have increasingly used compiled scores (scores with pre-existing music, typically pop).

Aspects

Film music can spell out the emotions you are supposed to feel.

Example: Gone with the Wind: When Scarlet implores Rhett, the music is weepy. When Rhett walks away, the music is momentarily jaunty. When Scarlet vows to get him back, the music is impassioned.

Film music can evoke emotions as an extension of connections that viewers already have with the music.

Example: The Royal Tenenbaums: Royal takes the two boys out and causes mischief, and “Me and Julio Down by the Schoolyard” by Paul Simon plays. The song is about three boys that have broken the law, so it is particularly appropriate.

Non-diegetic music is music that only the viewer hears (as in the previous examples).
Diegetic music is music that the characters hear. In other words, the music is part of the story. (The word diegetic comes from the Greek diegesis for narrative.)

Example: Lost in Translation: Charlotte and Bob sing karaoke and share a moment.
Example: Say Anything: Lloyd wakes up Diane with their song.

A leitmotif is a melody associated with a particular character or idea. Leitmotif technique derives from opera, specifically the operas of Richard Wagner.

Example: The Fellowship of the Ring: When Sam is about to step out of the Shire, the Shire Theme plays (1:26). When Frodo and Sam pass out of the Shire, the Fellowship Theme plays (1:40).

Further reading