A .png is a file format that allows you to save an image on a transparent background. Somewhat like a .gif in that respect, but it allows for a wider colour space than the .gif format, and somewhat like a .jpg, but this format is considered "lossless" file format. This file format can usually be opened by most of today's image editors - if yours can handle transparency, it will open these as simply as it opens any .jpg file; the only difference is you'll see a transparent background. This allows for easy insertion into other images.
The transparent background also makes it easy to use these file in 3D rendering programs like Blender or Bryce and makes them useful in flash files or animations, and using for animated gifs. These can be useful for adding bits and pieces into your own creations as well, like using for collage work, or placing on a white background as part of an ad-layout, flyer, business cards, flash games, jigsaw puzzles, educational games for children, and other similar graphics design work.
One of my favourite past-times (when I actually have a little time to just "play") is the newer variety of Hidden Object games - those that have a story and that require you to think a little about how to use the objects you collect. I've noticed some of my very own files used in these games, and it's one of the things that brings me a little delight - I'm usually pretty excited to find one of my images used in a game that I enjoy. That sort of occurrence usually spurs me on to creating more new .png files, because after all...nobody wants to see the same objects over and over again in each new game.