When directors are in the process of editing a film, temp music plays a huge role in how the scene is cut and pieced together.
In most cases, the film's composer will have sent the director and editor a piece of holder music to get an idea of the rhythm and momentum of the scene and will cut to that general speed and tone. Other times, directors have to work with existing music.
For example, William Friedkin admitted that he used Santana's Black Magic Woman when editing the famous car chase sequence from The French Connection and if you play the two together, you'll see how it synched up properly.
YouTuber SuperNoone89 placed Strauss' Also sprach Zarathustra - best known as the title music from Stanley Kubrick's 2001: A Space Odyssey, or Ric Flair's entrance theme - over the scene in The Matrix where Keanu Reeves' character, Neo, finds his power and realises he's the One.
Although it's not known for certain if the Wachowskis used the music when editing the scene, it seems pretty likely as it blends perfectly with the other and the two scenes have a lot in common - they're both at evolution.
The music is used in 2001: A Space Odyssey when the apes touch the monolith for the first time and discover the use of weapons and again at the end when the monolith appears to Dave Bowman and turns him into the Star-Child, and here in The Matrix, it's when Neo discovers that the world he thought was real was an artificial one.
Take a look and see for yourself.
Via YouTube