As others have said, often not much that justifies their budgets. They mostly function to issue tickets and raise revenue for the city, though I doubt that many high-budget police forces take in enough in fines to completely self-fund. (If anyone has precise data on this, I'd love to see it.)

But what they're intended to do is mostly deterrent. Be seen and therefore discourage people from breaking the law. You don't pass a cop on the highway, and if you know there's radar around you'll probably slow down. The problem is that as cops get a reputation for arbitrary stops and aggressive confrontation, some of the deterrent effect vanishes: "I could be good, but I'll get stopped anyway, so I might as well just avoid the police and do whatever I feel like. It's the same risk either way."