Rep is the user's reputation rating, showing how respected and well-known you are in the community. You can quickly estimate a user's rep by looking at the number of stars next to their rep value. Getting one or two stars is fairly easy, while five stars is a serious achievement.
There are a number of ways you can earn and improve your rep, including actively spending time on the GOG.com forums (no, that doesn't include spamming), receiving lots of positive ratings for your posts or simply helping other users (this can earn you lots of rep!). On the other hand, ignoring posting guidelines and rules is a simple way to lose tons of rep points (depending on how severe the violation was). Also, getting lots of negative feedback in a short time will cost you some rep points.