The power zoom is more like (in function not quality) what you might be used to in a point and shoot. You push a little lever forward and back to zoom in and out. The non power zoom is like a zoom lens on a dslr, you manually turn the lens to zoom.
Hi Kim The main difference between the two lenses is that when the camera is powered off the Power Zoom lens partially retracts and has a "pancake" profile. Powered down, the lens presents a 1.25 inch profile. Combined with a relatively slim camera like the gx1, the camera fits into a (bigish) shirt pocket. The lens also features a power zoom, so you get a nice smooth zoom- which is particularly useful for making videos.
The power zoom is also lighter, but you do sacrifice quality for the smaller size and lighter weight. When it first came out there was an issue with the lens which I believe was fixed with a firmware, but I'm not sure if the problem was completely fixed. It does use newer tech and elements so unless you're making posters, you should not have to deal with image degradation vs the non-power zoom. I use my camera basically as a point and shoot replacement so I'm not too concerned about image quality vs my DSLR.
The power zoom is a more convenient lens, generally speaking.