This was just recently asked by another new member...but that's okay, we're all newbies at one time and need answers.
The thumbs up and thumbs down are for giving approval or disapproval to another member and the result is a cheese - or a negative cheese if the person started out at zero (or so I would assume - I've never seen negative cheeses). So, if someone is particularly helpful or you think they've gone to extraordinary lengths cheese-wise, you can give them a thumbs up. If someone is discouraging or nasty, you can give them a thumbs down.
I really like the system and would love to have it available on other forums I frequent.
There is a section here of FAQs, I believe, with info for finding out how things work here - sorry I don't know the name of it off the top of my head.