Parabens are preservatives which can prolong the lifespan of a cosmetic product from around six months if it is wholly organic up to around six years. The cosmetic industry loves them for exactly that reason and swear blind they do no harm. There is a growing body of opinion that more research needs to be done on the long term effect of parabens, as no-one really knows what the long term effect on the body is after prolonged exposure to them.
Parabens are in pretty much everything from toothpaste, through all women's make up products and men's shaving products, it's hard to find something today that really doesn't have parabens in it, and when it does it tends to shout it out from the label.
I have no idea whether they are harmful or not to be honest with you, but try to avoid them simply because I don't know...