MP3 and ogg are compression algorithms for audio. Basically each take different approaches to achieve a >60MB file for one song ;D
Now here are the main differences:
Ogg is free, open source, and free as in oxygen.
MP3 is a proprietary protocol that is generally licensed. The whole hooplah over the past is mainly for companies who want to sell applciations, Linux distros that include the MP3 decoding codecs or apps, or hardware that can play MP3's.
Ogg is a better and newer protocol that is much easier on the CPU.