They read over one of their peer's papers (or other school-related project, but it's usually a paper of some sort) and proof-read it. They look for grammatical errors, as well as look to see if the thesis is supported throughout the paper and if the paper is clear and concise. They point out areas that worked really well, as well as points that need a little fixing.
I, personally, have a love-hate relationship with peer-reviews. On the one hand, it's nice to get another person's opinion, but on the other sometimes they tell you you should change or keep things that really shouldn't be changed or kept.
