I think you might want to know a little more than "MP3s are compressed (lower quality) audio files" and "WAVs are bigger..."
"Compressed" in this context means that the total size of the data file is made smaller by some process. (This is
not the same compression that one refers to when talking about compressing a track during recording using the audio processor known as a
compressor.)
There are basically two general ways to reduce the total size of the data. One is called
lossless because none of the original data is discarded, it is just represented in a way that takes up less space and the original data can be completely recovered. Zip files are a common example of this form of data compression. The other approach is called
lossy because, in making the file smaller, decisions are made about what data can be considered irrelevant, and this data is discarded. Some clever methods are used in these decisions and there are many forms of lossy compression depending on the type of data. Most are based on human perception and the fact that certain amounts of detail are more-or-less imperceptible so, if you discard the information, the result is perceived as acceptably close to the original, and the data file has been reduced so much, that it was worth the effort.
It's important to realize that once a file has been converetd to MP3 or any other lossy format like Real Audio,
the original file cannot be perfectly regenerated from the compressed file. Data is discarded in the process, and you can't get it back -- it's not reversible. So save those source files!
The parameters that are used to massage the data this way are usually adjustable, so one can apply more compression for greater file size reduction at the expense of fidelity. At some point you perceive that the quality has suffered so much that you've gone too far. You will find MP3s at all different levels of compression, and the ones that are compressed less sound better.
Why compress at all? It's a matter of storage space and bandwidth. Uncompressed data takes up more real estate on hard drives and other media. It also takes more time for raw data to be transferred across the internet, so the smaller you can make it, the easier it is to transfer from place to place.
Data compression is used in all kinds of applications, notably digital video (the audio and the video on consumer DVDs is compressed so that all the data can fit on the disks) and photographic images (the ubiquitous JPEG format is a lossy compression format).
As far as "what can be done with each," well, WAVs are typically used for recordings, and audio CDs are made using a variant of the WAV format. In other words, the raw recording made on a PC running SONAR or Pro Tools is made in WAV form, and when a mix is made, it is exported as a 16-bit, 44.1 kHz stereo WAV file so it can be burned to a standard audio CD format directly.
For putting on the web, or sending a song to someone via email, or to allow four or five hours of music on a MP3 player or a data CD that can be played by an MP3-capable CD player, one encodes the source WAV file to an MP3 file.
