A door is a moving structure that when closed acts as a barrier to a room, house, building, or car. You'll have to open the door to let your dog come inside.
Buildings have doors, and so do most vehicles. You might also have a special little door built into your own back door for your cat. Doors act as security, as they can be closed and locked, and also as ventilation when you open the door to let the spring air in. Being "out of doors" means you're outside, beyond all the doors of your house or building.