TVtropes has an entry for Climactic Music
Narratives have climaxes. So do their musical scores. In the case of Climactic Music, the music's climax coincides with and characterizes the narrative's.
The swelling, booming music will help add tension or triumph to the scene.
As a bonus, I will add that the credits list none other than Ennio Morricone, one of the greatest composers of our time, as composer for In the Line of Fire.
The link I provided earlier, mentions the duels at the end of each of the Dollars trilogy that Ennio Morricone is well-known for.
Another example of Climactic Music is "Duel of the Fates" which was used during the final fight in the Star Wars Episode I "The Phantom Menace". Written by John Williams, it is a little different than what you refer in that it will include a choir but still remains a musical piece matching the action of the film.