A Door in Diablo series is generally, like in real life, a moveable obstacle that gives access to another area, often a room or a chamber.
All doors can be opened by clicking on them. Most monsters cannot open doors, but the player's minions can. Doors are often used as bottleneck points to split enemies and fight them one by one.
Some doors can be broken by damage, while others can only be opened manually.
In the first two games, any door that was previously opened (not with force, obviously) can be shut again, but only if no objects, players and monsters are in the doorway (it will be dubbed Blocked if anything is). Corpses can block doors too.
Skills that force movement (such as Steed Charge) cannot carry heroes through closed non-breakable doors.