MP3's and JPEG's are the same kind of files, only they store different data (well, in a way they are). They both take an uncompressed picture/sound file and compress it in a way that saves space with some loss of quality. JPEG's use algorithms to alter the different patterns that will make up a picture, and MP3's selectively throw out little bits of data that aren't completely necessary. However, making a JPEG/MP3 out of another JPEG/MP3 compounds the compression so that you end up throwing out more data than you would like, and you end up with crap.
You've probably seen plenty of bad pictures online, not because of the content, but because they were full of artifacts. The same goes with MP3's.