Azureus has been fine for me ive never really used anything else.
A torrent is a large file which can be downloaded by a 'link' provided by many sites. The small file is opened up into a 'client' where it can be downloaded. Similarly to file sharing you need people to host the file these people are called seeds and then there a leechers who download the file on the seeds. And then there is a share ratio thing which is important as it can affect speeds etc basically the ratio of upload/download.
i go straight to mininova or isohunt to download my torrents, there are useful forums around which document torrent releases specficially to the type of file e.g. movies, sports, television shows etc might chuck a few links later.