It is a little technical, but even if you just look at the pics, you can see some of the differences between formats.
A quick summary:
- .gif and .png have the ability to have transparency.
- Only .gif can be animated.
- .tiff is superior for amazingly high quality.
- .jpg is the most commonly used due to it's good quality, yet small file size.
- .bmp has huge file size and thus is rarely the best format to use. An exception would be that it is a Windows wallpaper format.