Great question! I'm really fascinated by evolutionary psychology (although I don't know much about it), but a quick bit of research on this question shows there are many theories as to why music is so important to us.
My favorite is that "music exists to give evolutionary psychologists work".
But in all seriousness, there are some very practical and tangible benefits that music provides. Any one of these could have been a driving force behind music's evolutionary endurance and the subsequent ubiquitousness it now enjoys:
- Courtship and mating ritual and behavior (think mixed-tapes, serenades)
- Soothing fear and calming (lullabies, whale song)
- Group bonding and solidarity (today, taste in music divides people into tribes, but also think of rowers moving in unison to the beat of a drum)
- Assisting humans in tuning their hearing (humming in different pitches could have been a good way of preparing for a hunt?)
- Reduced conflict within the species. Pastimes like singing or dancing rarely result in conflict and casualties, so communities that sing and dance together have less time for killing each other.
- Passing down of information and oral tradition. A means of communication
I guess we can't say for sure why music has become such an important part of human culture, and there are of course humans that function perfectly well and have no time nor affinity for music.