"Why did she leave her car there?"
This is a loaded question. It says something is true, and then asks a question about it. It doesn't just ask why, it' also says that "She left her car there."
"Why would she leave her car there?"
This question is hypothetical. It asks us to imagine a situation that may or may not be true. This question still makes sense even if she doesn't have a car.
We can still use the "would" question even everyone agrees that she left her car theree. In which case as other answers have said, this means the question is allowing free speculation rather than asking for a certain answer and this is a subtle distinction that many people would not make.
If her leaving her car there is not accepted by everyone involved in the conversation then the distinction between a loaded question and a hypothetical question is very significant.