You can't do anything with them. It only shows how active you are on chess.com.
Points(Очки)

Once upon a time when chess.com was new and Erik wanted to encourage folks to post in the forums, he gave away free Tshirts for X number of points.

Here you go mate, just the thing for impressing the girls:
http://www.wholesalechess.com/shop/chess-supplies/chess-shirts/chess-com-t-shirt
Hi All! Please tell me that for points of activity, which I have at the moment 402? As they charged? Can be anything to do with them?(Привет Всем! Подскажите пожалуйста, что за очки активности, которых у меня на данный момент 402? Как они начисляются? Можно что-нибудь с ними сделать?)