A Citizen is any character living in any city, hold, or province that is not associated with any guilds in a major way. The player may also be a citizen in a city or hold, so long as that player has met the requirements do so.
Usually this is done by completing a quest or series of quests, followed by purchasing the home (see Houses (Skyrim)/Houses (Oblivion)/Houses (Morrowind)). A guard is likely to call all residents or visitors to a hold/city/province Citizen, regardless of them actually living in aforementioned area. Citizens are different in every city and hold. Many Citizens will be able to become a follower to the Dragonborn, but only if their side quest is completed. They will be hostile to the Dragonborn if they have previously stolen from, or assaulted the Citizen.