They often mean the same thing, but "incredible" is much broader term with a wider variety of possible meanings.

They can mean the same thing depending on the context. "Incredible" generally indicates some kind of awe or surprise (usually in a good way) in a reaction. (for example--being in awe at someone's incredible skill) "Mind-boggling" indicates that something is so different or unexpected that your mind has trouble understanding it. This is also just my opinion, but to me, "mind-boggling" is a little less formal than "incredible."

They are not really the same. To begin with, "incredible" is a more common, everyday word; it's basic vocabulary. "Mind-boggling" isnot. Although it literally means "unbelievable," "incredible" often means extraordinary, amazing--or, simply, extremely good. "Mind-boggling" describe something that your mind actually cannot accept. A good example would be M. C. Escher's picture, "Ascending and Descending." Do a web search for it. In this picture, you see a staircase which goes around four sides of a square. As the people walk around it in the clockwise direction, they are obviously going upstairs. Yet when they go around all four sides they are back where they started. Meanwhile, people walking counterclockwise on the same set of stairs are obviously going downstairs. And yet, they too, end up in the same place, no lower than where they started. You follow the staircase with your eyes. It is going down, down, down--and then suddenly you realize it has joined itself. That moment of surprise is your mind "boggling." Another example of something mind-boggling is the proposition, in mathematics, that two times infinity equals infinity. "Huh? That's impossible. That can't be true." Your mind "boggled."

I think mind-boggling is a bit stronger. The synonyms given for it are "overwhelming" or "startling". It's something that really surprises you. Whereas "incredible" means like "fantastic," "wondrous," "grand," or it can mean "difficult or impossible to believe". If something boggles the mind or is "mind-boggling", that's a little bit stronger than incredible. But they are close in meaning.