Question

What do we do with our "points" on this site?

Answer 1

Short version: we don't do anything with them, we just have them to show others how much we have answered.

Long version: points are simply a means to show experience and credibility. You can't buy anything, but it signifies to other users how experienced you are with answering questions and therefore how much your answer can be trusted. This is not to say that someone with more points is smarter than someone with a lesser number of points, just that the person with more points has answered more questions. points also determine, in part, your "rank." Mine, for example. is expert. this has no other benefit other than letting others know how credible your answers are.  

Answer 2

Step 1:
You look at them from this angle, then from that angle, you smile
and say to yourself "Not bad, self !  Not bad at all." 

Step 2:
Then you step back for a better view, and admire them some more. 

Step 3:
After a while, the novelty wears off, and you want a stronger kick,
so you answer some more questions, and get some more points.
Then you have a higher number to admire, so you go back to Step 1.