Assuming you haven't looked it up already, it has to do with peer-to-peer file sharing. When you download a torrent file, what you get are trackers for peers who have the target file that you want on their computers (and in their torrent clients). Once you have downloaded all or part of a torrent, you are also sharing what you have with people who don't have it (having only the trackers and/or the other parts of the file). "Seeding" refers to leaving your trackers active after you all or part of the file, allowing others to get it from you, whereas "leeching" is downloading only and not uploading to share in turn. It is considered a common courtesy to seed the file for a period of time once you've finished downloading your copy to further its spread and help other people download it in turn.

TL;DR: It's polite to leave your torrent trackers up for a while after your download finishes so other people can get the file too.

Hey, Rarity and I actually have something in common!