A door is a way to go through a wall. Only players can open and close doors. But some of them are locked, and maybe a key will open them.
Some doors are actually Gates of Expertise, and have certain requirements to be opened.
Other mysterious doors are ones that say "The door seems to be sealed against unwanted intruders." These doors are involved in various quests, and cannot be opened until you have either started or completed the quest for that particular door.
Many doors have mailboxes behind them, and can only be opened once you have completed the Postman Quest.