A RPer is a roleplayer, one who likes to play RPGs, also known as role playing games. More specifically, a RPer is one who is in character, and not just attacking people like the computer would. I'm not a big roleplayer myself, (HA!), but an example would be like:
Player1: I see you need help crossing the river. For 50 ore I will give you a ride in my shuttle. It's only one way. If you need a ride back, just whistle.
Player2: Agreed.
Actually, I have no idea if I'm anywhere close lol.. But you act in a character mode. If you're talking out of character (OOC) then you usually put []'s around it or some way of letting them know you're talking OOC. The character mode is set by the name of the RPG and by the character you select (Whether in game or the slot in the screen where the host can boot/ban)..