Parabens, it's hard to avoid the topic of much debate these days. Well, let's start with the first part of your question: What are parabens?
Parabens are preservatives found in many skin and body care products. Preservatives are what enable your products to have a long shelf life. You can tell if your product has parabens by looking at the ingredient list. You may see one or more of the following: Methylparaben, proplyparaben, isopropylparaben, isobutylparaben, butylparaben, sodium butylparaben. As you see, each word ends with "paraben", which makes it easy to pick out.
Your second question, should you avoid them, is a bit of a personal choice. I can tell you why people are choosing to avoid them and then you can make your decision.
Parabens have been found to mimic estrogen. This, to some is cause to believe that they are a possible trigger for cancer, especially breast cancer. The FDA has come to the conclusion that at this moment, parabens are a safe ingredient in skin care products and that there is no cause of concern. They will continue to do research and alert the public if this changes.
Many smaller skin care companies proudly state the fact that they are paraben-free. While this is a great option for them because of the smaller quantity of products they make and sell, most larger skin care companies use parabens to enable you to get your supply of product no matter where you shop.