Bittorrent works by having a starter file, called a torrent that you download to your system. It basically has the "layout" of the file/files your downloading. Information like sizes, m5sum values, etc. Once you download the file and launch it in your bittorrent client it then sends a ping back to a tracker located on a central server which makes it much easier to grab the file from anyone using. By grabbing I mean it works entirely distributed. Instead of downloading a file from one location, it takes peices from everyone, anywhere who has the file. Speed wise it has the potential to be quiet fast though most of the time I've noticed its slower and uses a higher CPU utilization than Direct Connect or the like. It also will upload peices of the file the second you get it. So basically, the second you get a bit of it its sharing that out to others. Highly effiecient bandwidth sharing.
DirectConnect is much more centralized, like Napster. You have everyone connecting to a central server to see each other then making a connection between each others computer when they share files. Its faster than Bittorrent but much easier to take down/limit. Otherwise, the second you make a connection it becomes entirely peer-to-peer. Individual.