JPEG/JPG
Short for Joint Photographic Experts Group, the original name of the committee that wrote the standard. JPG is one of the image file formats supported on the Web. JPG is a lossy compression technique that is designed to compress color and grayscale continuous-tone images. The information that is discarded in the compression is information that the human eye cannot detect. JPG images support 16 million colors and are best suited for photographs and complex graphics. The user typically has to compromise on either the quality of the image or the size of the file. JPG does not work well on line drawings, lettering or simple graphics because there is not a lot of the image that can be thrown out in the lossy process, so the image loses clarity and sharpness.

GIF
Short for Graphics Interchange Format, another of the graphics formats supported by the Web. Unlike JPG, the GIF format is a lossless compression technique and it supports only 256 colors. GIF is better than JPG for images with only a few distinct colors, such as line drawings, black and white images and small text that is only a few pixels high. With an animation editor, GIF images can be put together for animated images. GIF also supports transparency, where the background color can be set to transparent in order to let the color on the underlying Web page to show through. The compression algorithm used in the GIF format is owned by Unisys, and companies that use the algorithm are supposed to license the use from Unisys.^*

PNG
Short for Portable Network Graphics, the third graphics standard supported by the Web (though not supported by all browsers). PNG was developed as a patent-free answer to the GIF format but is also an improvement on the GIF technique. An image in a lossless PNG file can be 5%-25% more compressed than a GIF file of the same image. PNG builds on the idea of transparency in GIF images and allows the control of the degree of transparency, known as opacity. Saving, restoring and re-saving a PNG image will not degrade its quality. PNG does not support animation like GIF does.

^*Unisys announced in 1995 that it would require people to pay licensing fees in order to use GIF. This does not mean that anyone who creates or uses a GIF image has to pay for it. Authors writing programs that output GIF images are subject to licensing fees.

For further information on these graphics formats, see:

GIF vs. JPG -- Which Is Best?
GIF, JPG and PNG -- What's the difference?
Myths and Facts about JPG
File Formats
RFC 2083: PNG Specification