BitTorrent has got something of a bad reputation these days, being used for much of the illicit traffic of copyrighted material, but it has good legitimate uses too, particularly for Linux users. Anyone who has tried to download a new distro version on the day of release will know how overloaded their servers can be, BitTorrent often gives faster downloads and you can do your bit to help by seeding after download is complete.
Deluge is different from most other BitTorrent clients in that it uses the classic Linux client/server setup. The server sits in the background downloading and seeding the torrents while several clients are available to add torrents, watch progress and do the other things you do with a BitTorrent client. This has two main benefits, the first is that the server is always running, you do not need a client running on your desktop (or even a desktop open) to be running torrents. The other benefit is that if you have more than one computer, and what self-respecting computer enthusiast doesn't, you have the one computer running the server to handle the torrents while you can run a client on any computer, even from outside of your network if you have a suitable router setup.
The GUI client acts like most other BitTorrent programs, so you should feel immediately at home, but there is also a command line client and a built in web server to manage your torrents from any browser. The GUI client, using GTK, is nice to use but nothing particularly special in this field, but being able to manage one collection of torrents from several places gives Deluge a special advantage.