Hopefully third time's the charm...
Torrents are a distributed distribution network. When you begin to download a torrent you become part of the swarm. Members of the swarm will request pieces that they do not have from others in the swarm, so as time goes on, you will be both up/downloading. The advantage of torrents is that they spread the responsibility of the 'host server' to several (if not hundreds) of individual pc's.
A leech is a person who only downloads (or has a pathetic upload rate). Many clients keep track of your share ratio, your upload:download ratio. As your ratio improves (gets closer or exceeds 1:1) you will typically get better download speeds.
The legality of the downloads comes down to the files themselves. If you see a torrent marked 'Office 2007 with crack' it is obviously an illegal file and the crack may crack more than just the copy of Office, so beware!
EDIT: Others such as open office, firefox, and many other open source files are just fine for torrent downloads. Odd are if it's free, they don't mind the torrents as it keeps people off their main download servers and as such saves them money.
As for the lawsuits, they have been mostly against the torrent trackers, and most of those have failed to hold up in court. Torrent trackers are just search engines for a specific type of file.