Interior commonly refers to the inside of something. When house hunting you might find that the outside of the house is run down, but the interior rooms beautifully renovated.
If you design the color scheme of a room and pick our furnishings for it, you are an interior designer. If you delve into a characters feelings and emotions, you might describe what you're looking at as their interior. A place that lies far inland from a coast or border is said to lie in the interior of a country. If you talk to yourself inside your mind, you are said to be having an interior monologue.