Roleplaying characters are one of the two types of characters that can be created in Guild Wars. These characters are also called PvE (Player versus Environment) characters. The other type is a PvP-only character. In short, role-playing characters, with a bit of effort, eventually have access to both PvP and PvE, whereas PvP characters may only access PvP content.
Roleplaying characters begin at level 1 and can play in both the PvE and PvP areas of the game. Each roleplaying character is linked to a particular campaign, which determines the start location, the available character models, and the initial skills. After progressing a certain amount, any character can move between other campaigns to follow the storyline (provided the campaigns are purchased on the same account).
A roleplaying character is the archetypal RPG character: they are created "from scratch" at level 1, and must gain experience by doing quests, completing missions, defeating foes, and following other adventures in order to become stronger, unlock new skills, and buy new and better equipment. The character's reach also expands as they continue in the storyline and discover the various realms of their world.
Roleplaying characters may also partake in any unlocked PvP battles, provided they meet whatever requirements exist (i.e., preliminary quests or level restrictions). During the course of regular PvE play, they also unlock skills and items for PvP-only characters on the same account.
To enjoy the entire game, it is worthwhile trying both a roleplaying and a PvP-only character. Since every copy of the game comes with multiple character slots, you can have both at the same time.