A BitTorrent Client is a program that will manage all of your downloading and uploading you do using torrents.
There are many clients out there, each offering different pros and cons. Only use one client at a time, as using more than one won't make your speeds better or anything.
Here is a list of
recommended clients you can use:
Here are some more clients:
For a large list with comparisons of features between clients, click
here.