Why did she leave her car there?
This is asking for a definitive statement. (She was drunk and didn't want to drive.) One that indicates the actual reason for her having left the car there.
Why would she leave her car there?
This is asking for speculation. (Somebody paid her to leave it there. Aliens made her forget about it.) There could be any number of possible reasons for her having left her car there. (Although the aliens one is highly unlikely and I only used it as an example.) All of these could be an answer to the question.
Once she (or somebody who actually knows) is asked, speculative answers can be confirmed or denied.