it can be a bit daunting to start, so i will give you the bare-bones details, then point you to a very good guide.
Torrent: a file containing information about what you want to download, where to find people that have the files to upload TO you
Seeds: people that have the files you want, and can upload to you
Peers: people like you that do not have all the files, and are in the process of downloading from seeds, and uploading to other peers
limewire: a lousy program that is only good for downloading single song tracks, and still not very good at that.
mininova: a site listing hundreds of thousands of Torrents (see above) for you to download
Azureus: not a babies' client. probably the best out there in my opinion, the one you should likely use while being on a mac, as it's plugins and options will help out later when you learn more and want to protect yourself, and maybe even upload your own torrents :)
note: with the aforementioned client, it will be wise to first click the 'Advanced' button in the top right on first startup, then go to tools>options>interface>start> click 'Show' and select 'Advanced' for starting up, then you will have the normal view and not the 'Vuze' Layer that is mostly for downloading of hi-def media content, but not good for managing your up/downloadsDeluge: a lightweight client, that will do a lot, but i have heard is easier for people just starting out
when downloading torrent files, you want a good Seed-to-Peer ratio, such as 500 seeds and 1000 peers is relatively good, as it comes out to 1:2
40 seeds and 2000 peers is not good, as it is 1:50 and will produce very low speeds for download
also remember that when downloading, it's best to give your client time to find seeds and peers and go through a full tracker check (tracker is the server that connects peers and seeds together) which can range anywhere from 10-30 minutes time.
when you first start a download, it's not uncommon for it to be slow, but as you get more of the file(s) you intend to download then you have more to offer others and then your "priority" in the swarm (the entire group of people sharing the files) goes up and you get files faster from other people, the faster you upload, the more you will get from people that have all of the file(s)
i hope this helps you
M00ter's Bittorrent GuideHowto: get good download speedsif you want to start uploading your own torrentslet me know if you need any further help
M