BAHA stands for: Bone Anchored Hearing Aid.
It's mostly used for people with single-sided deafness or those who, for whatever reason, cannot benefit from wearing behind the ear hearing aids.
I'd rather send you to a source, than paraphrase and possibly send false information. (even though I have one, I'm no expert. My parents got it for my birthday one year and I just benefit from the thing!)
I'll just link you to the wiki-page and "official page" - that's another reason I was confused, the official BAHA page is on CochlearAmerica's webpage.