Why compression? The answer is: space. Or better: disk space. Images are kept in disk files, and floppy disks or hard disks are finite spaces to keep data. And, as we do graphics for on-line media, another dimension comes into effect: time. The more space an image takes on a disk, the more data must be moved across a network until the readers of a web page see it - and the longer they will wait for it. Although the typical computer lab network connection is rather fast, especially in the case where all the readership is on campus, you might consider those thousands of students who use their modems to access the Internet from their home. Their data connection is much slower than the average computer lab.
How does it work? Compression algorithms is a science for itself. There is a variety of rather simple algorithms 
, but more sophisticated
formats like JPEG use complex mathematical analysis to find regularities in color variations to store common characteristics. The latter
kind of algorithm gains several times more space than the first one, but needs some care when using it. And the better the algorithms work, the
more computer power is necessary to process it. Viewing JPEG images with a 1986 IBM compatible personal computer would be rather slow.