There exist black holes in the universe because any star which is greater than 3 times solar masses can go into three types objects in their final phases.They may be white dwarf,neutron star or black hole. So forming a black hole is an inevitable phenomenon In our cosmos.
Now turn to the main question, why?
Because black hole regulates star formation in it's host galaxy. There is a huge correlation between black hole and galaxy co-evolurion. So without black hole, galaxy might not be fully structured.
In center of each galaxy ,there is a supermassive black hole. It preserves angular momentum of that system. When there exist too many masses in a small region,they don't let go anything outside nor even light. So these masses creates curve in space-time curvature and gravity is too high.This high density region is known as black hole.It is also a consequence of theory of general relativity by Einstein.
So existence of black hole in space proved by theoretically and experimentally both.