JPEG (pronounced "jay-peg") is a very common image compression format. The letters "JPEG" stands for Joint Photographic Experts Group, the original name of the committee that designed the standard. The JPEG format was designed to handle full-colour photographs and other "natural" pictures. As such, it works well on photographs and natural artwork such as paintings, but performs less well on lettering and line drawings.
JPEG is a "lossy" format, meaning that JPEG images aren't the same under close inspection as their original. However, the JPEG format was designed to fool the human eye, so very often you will find uncompressed and JPEG-compressed images looking very similar. A unique property of JPEG is that the degree of compression can be varied, which allows the image maker to trade file size against output image quality. Very small files can be achieved if you don't mind awful quality!
One minor drawback to JPEG pictures is that they don't guarantee exact colours, which means corporate logos and other images that usually require very exacting colour standards are often not suitable for JPEG.
A more advanced JPEG format has recently been released, known as JPEG 2000. This new format supports much more complex compression - including variable compression across an image - at the expense of speed.