One way the music can be used is to unify a mosaic of scenes, giving them a common mood and meaning. A wonderful example is from The Lord of the Rings. In this scene, Lord Denethor has knowingly ordered a hopeless attack, weakening his city to guarantee the death of his son and the end of his own line. The visuals shift from Denethor to the attacking forces to the defending forces to Pippin, a hobbit, who sings a song from the perspective of eternity, that everything must "fade" and end.
The ultimate montage to music, though, is the second scene in the film The Watchmen (2009). It contains a sequence of images from May 1939 to some time in the 1980's, when the story itself is set. They show a world that is subtly altered from our own. For example, the plane that bombs Hiroshima is called the "Miss. Jupiter" instead of the Enola Gay; for example, the famous photograph of a sailor kissing a nurse on VJ Day has a superhero(ine) replacing the sailor; for example, the Zapruder film of John Kennedy's assassination now shows the identity of the assassin. The music that ties this together, reflecting the changes from our timeline, is, of course, Bob Dylan's "The Times They are A-Changin'."
I'd embed a clip of this, but these clips are being aggressively taken down from Youtube. Here is a link to it on Vimeo instead.
Another way to use the music is to match the mood of a wordless scene, as in the excellent movie Truly, Madly Deeply (1990). The story is of a woman whose husband has died, and she is not coping at all well. Her grief is intense and unrelenting, to the point that her husband returns to her from the dead as she plays a piece of music that they must have often played together, Bach's Sonata No. 3 for Cello (Viol de Gamba) & Piano.
The romantic comedy LA Story (1991) also has two musical highlights, both performed by Enya. The first is when the two main characters realize that they have fallen in love.
The next is when she is about to leave, and all the elements rise up to prevent her flight.
My last video in this post is from a fairly obscure movie called Iceman (1984), in which a neanderthal is brought back to life. The scientist and his subject have no language in common, of course. Any communication has to be emotional. For example, through Neil Young's music.
I could go on. These film clips are a selection of moments in film where music rolls up its sleeves and reveals its strength. If there are other moments that come to mind, let me know in the comments.