Ok, I'll tackle this but will not duplicate anything the can be answered in the first 10 links of the above google search.
"Okay... I must first mention that I have a MacBook Pro AND a PC still using XP (Vista's a little scary). I know there are separate forums for PC and Mac, but I wanna know for both and it's not like there is a joined one. Perhaps BitTorrent works the same for both... I don't know."
That's an easy one. It works the same. For an example, look at Azureus. Same code for all platforms.
"I tried reading the Wikipedia information on BT, but my questions weren't exactly answered."
Let's keep reading your post and find the questions.
"My biggest question is: Does BitTorrent work, even when the program isn't actually on?"
ABSOLUTELY. Even when your machine is not participating in the "swarm" the others are exchanging "packets" and making the file or whatever the torrent is about more available. Even when you are not running it, others are still swapping "packets."
"Anyone get where I'm going with this? I just want to make sure that it's not being evil and slowing my Internet connection down. I'd appreciate any help."
Now you've hit on an item that some complain about. Since torrent traffic can be quite big, some ISPs or others may complain that torrent use does take up bandwidth of the "internet". But my thought here is that spam does a better job of that.
Hope this helps,