Parabens are preservatives. They are what keeps your shampoo, blush, mascara, shaving cream, deodorant - any beauty or hygiene product, really - looking and feeling the way it should for as long as it lasts. Parabens are cheap to produce and are effective at what they are supposed to do.
So, what is the problem with them? Well, they have been linked to cancer - specifically breast cancer in women. While it has not been definitively proven that parabens cause cancer, they mimic hormones and it is a fact that exposure to estrogen is closely linked to breast cancer. Incidence of breast cancer in men as well as testicular cancer are on the rise. If there is a chance that your body lotion or soap could be connected to cancer, do you really want to keep using it? I don't. There's a high rate of breast cancer in my family. If I can reduce my risk, even just a little, bit by avoiding parabens, why wouldn't I? Lots of companies are wising up to consumer demand and removing parabens. Paraben-free products are readily available. It's up to you to avoid them, all you have to do is read the ingredients!
I got my info here: http://www.besthealthmag.ca/look-great/beauty/parabens-what-are-they-and-are-they-really-that-bad