It's the acronym for Butylated Hydroxy Anisole. It's a synthetic antioxidant that's used as a preservative.
It's a somewhat controversial ingredient: The U.S. National Institutes of Health says that BHA is "reasonably anticipated to be a human carcinogen based on evidence of carcinogenicity in experimental animals" (source: wikipedia). But, and this is a big but: these experiments were made on animals and BHA was used in high doses as part of their diet. There is no evidence that the same is true when used in tiny amounts in cosmetics products. So you probably have nothing to worry about, but if you are a better safe than sorry type there are plenty of nice products without BHA to choose from. :)