I do not know the context in which you noticed this expression, but it probably relates to "Alice in Wonderland". Alice chased a white rabbit down its rabbit hole and encountered a make-believe world. So the rabbit hole is a metaphor.

What is the context? Is this part of a longer passage?

As it is, I would think that it is referring to being in a very unrealistic or unpleasant situation. Maybe someone who is going through a lot of problems at the moment may say that he or she is far down the rabbit hole.

The term "going down a rabbit hole" usually means the same thing as "going on a wild goose chase". Both refer to following the wrong path when looking for something.