Torrent downloading involves many machines connected together in what's called a peer to peer network. Each of the machines has an amount of the the fileset to be downloaded, over time each of the machines increases the amount it has by virtue of swapping bits with each other. First there is one complete copy then two, three, four etc as newcomers to the network complete the data transfer from the peer machines in the network. This is different from the iTunes model where a client downloads a file from pool of files held on one machine.
To download torrent files you need a torrent client like Bit torrent or Azureus. You then open a "seed" file which contains information as to where the file is held. The torrent client then connects to the peer to peer network, downloads and collates the data.
Torrent files are often used for pirated music and video but also have a legit usage for large file transference. Legit usage examples include BBC iPlayer, transfer of Linux images etc.
Hope that helsp some.
Cheers Mike