What does she's barking up the wrong tree mean?

It may help to think of it this way:

A dog chases a squirrel. The squirrel runs up a tree. It then (unseen by the dog) leaps to another tree. If the dog continues to pace around the base of the original tree barking and whining at nothing (since the squirrel is no longer there), that dog is barking up the wrong tree.

When used of humans, it generally means something like "she's trying to get something from a person who doesn't have it" or "she thinks a person has/is something, but he really doesn't/isn't."