Roleplaying (RPing) is acting as if the player was actually the character that he or she plays. Instead of simply controlling the actions of the character in game, roleplaying players talk as if they were the character, create background stories, and act like they believe their character would act under given circumstances.
For example, a player might create a doctor character, and then might create a backstory, describing where the doctor worked before the epidemic broke out, and how he or she is taking the whole situation emotionally. This player would probably remain close to the hospital described in their backstory, and make in-game decisions and actions that relate to the character's personality rather than that of the player, ranging from minor choices as staying in an invaded hospital to defend it to the death, to more important choices as what type of weapon to use, and what skills to take or not. Another example would include a scientist character, creating a backstory that includes how he ended up joining Necrotech, where he's from, how he feels about the outbreak, and include lack of physical strength. This player might make choices to run from a zombie break-in rather than stand and fight, and probably would use firearms and decline to take the Body Builder skill, or carry a flak jacket, to further indicate the character's lack of physical ability.
In Urban Dead, a lot of roleplaying is done outside of the game, on the Unofficial UD Forums. Roleplaying is also done inside of the game, with the use of various features such as speaking or spraypainting. It is often assumed that when characters speak to each other through metagame channels they have some form of radio in order to communicate, or have messages delivered by runners or scouts in the case of some larger groups.