The type of compression we've been discussing here is called lossless compression, because it lets you recreate the original file exactly. All lossless compression is based on the idea of breaking a file into a "smaller" form for transmission or storage and then putting it back together on the other end so it can be used again.
Lossy compression works very differently. These programs simply eliminate "unnecessary" bits of information, tailoring the file so that it is smaller. This type of compression is used a lot for reducing the file size of bitmap pictures, which tend to be fairly bulky. To see how this works, let's consider how your computer might compress a scanned photograph.
A lossless compression program can't do much with this type of file. While large parts of the picture may look the same -- the whole sky is blue, for example -- most of the individual pixels are a little bit different. To make this picture smaller without compromising the resolution, you have to change the color value for certain pixels. If the picture had a lot of blue sky, the program would pick one color of blue that could be used for every pixel. Then, the program rewrites the file so that the value for every sky pixel refers back to this information. If the compression scheme works well, you won't notice the change, but the file size will be significantly reduced.
Of course, with lossy compression, you can't get the original file back after it has been compressed. You're stuck with the compression program's reinterpretation of the original. For this reason, you can't use this sort of compression for anything that needs to be reproduced exactly, including software applications, databases and presidential inauguration speeches.
For more information on file compression and related topics, check out the links below.