PVC damage on coins is caused by the breakdown of the polyvinyl chloride (PVC) that is found in inexpensive plastic coin packaging. The most common source of PVC damage is storing coins in plastic fold-over holders called flips. There are two basic types of coin flips: the soft, pliable kind (which contain PVC) and the stiff, brittle kind made of Mylar (often referred to "unplasticized" or "non-plasticized.") The PVC is added to the plastic to make the flips easier to handle, but if you store you coins in the soft plastic flips you risk damaging their surfaces when the PVC breaks down chemically.
Other types of coin storage media can also contain PVC, including cheap, Chinese-made coin albums and storage sheets, coin boxes, and certain display packaging. In general, if the plastic is soft, it probably has PVC. You should never store your coins in any kind of storage media where you can smell the plastic!
Most experts will tell you that PVC residue should be removed by a professional coin conservator, but you can do it yourself if you are careful. I have instructions on how to remove PVC residue from coins, and if you're wondering what the heck this PVC stuff is all about, check out my FAQ, "What is PVC Damage?"