Peened refers to "mushrooming" the end of the pin, so it acts more like a rivet. When you push the chain pin out using a chain removing tool it sheers of this edge (see the link I posted above). You can actually see a small sliver of metal. Pushing the pin back in won't reseat it as well and the link can fail. Not all chains are peened. There is a special connecting rivet you can use for Shimano chains.

If you're using a fairly low cost 1/8 KMC, you're probably fine. According to KMC's site, the higher end chains are peened to help resist side to side motion. I can't seem to find information on whether individual chains are peened or not. If so, they'll have peening marks on them and the pin will look like a little mushroom head rather than the end of cylinder.

edit: Looking at KMC's site http://www.kmcchain.com/index.php?ln=en&fn=find, find your chain. When you go to the individual chain information, you'll see a few icons along the bottom for many chain types. One is a circle with two lines. On mouse-over it says "High Pin Power". This probably refers to a peened chain pin.