mp3's are songs that are ripped (recorded, sorta) from a CD to your computer. The Ipod is a device that can play mp3's as well as some other media files- some movie files and other music filetypes (I think .wma's). It used to be hard to find software that allowed song ripping- now most music programs include it. WinAmp is one of the most well-known (and free) programs used to listen to .mp3's that are on your harddrive.
Mp3 is just a filetype, honestly, just like .jpg or .gif - and music can be ripped into may different filetypes. The Mp3 filetype is just one of the most commonly used ones. IPods are supposed to be used only with music that is bought- either you own the CD, or use a pay-to-download fileservice- Itunes is ment to be used, mostly, but Napster is another. However, alot of people download illegally via peer-to-peer file sharing programs, like Limewire (currently suffering a major lawsuit), KaZaa, BearShare, and I'm sure others I don't know about. I think KaZaa was destroyed in the round of lawsuits that hit it and Napster a few years back- Napster reinvented itself as a pay-to-download service, and survived. There was another I can't recall the name of that was recently killed, other then Limewire. The peer-to-peers don't just cater to music downloads, either.
Dunno anything about Blackberries or TiVo... LOL