What causes knuckle "popping" and the feeling of relief that comes from it?
Nobody really knows where it comes from. The currently most popular theory is that pulling the joint apart leads the gases in the joint's cartilage to accumulate and form a bubble which then pops when you let it spring back. The only thing that has been researched is whether it has an effect on the joint, but people who do it regularly don't seem to have any problems with their joints more than anyone else (I'll find the reference once I have time). Apart from that it's hard to get funding for this kind of research because it has little practical use.

Relief like feeling? That must be subjective to you, I used to do it every now and then but I don't remember getting any relief from it. In that case, it's probably the same relief as other people get from picking their nose, their ears, biting their nails, etc. It's called compensation reaction.