Yes, torrents are very small files that contain information about the file you want to download.
With normal downloads, you choose to download for example example.zip. You get the zip file, and can use it straight away. You download straight from the server (computer) that has that file on it. Everyone downloads from that same server.
Now, if I tell you that letting people download from your public server costs money, you may realise what trouble we could now be in. What if there is a really popular file that everyone wants to download? They'll all download from the same server, and will either overload the server, or cost its owners lots in bandwidth costs as they have to supply this file to everyone. Not too good.
Solution: bit torrent! You download a very small .torrent file from the central server (this is ok even if its very popular, as the .torrent file is very small). You then use a special program (such as azureus, linked above, and my favourite bitTorrent client), which takes this .torrent file and sees where to download the actual file you want from. The .torrent may be linking for example to some large program that is 100MB. This torrent client program sees what server has the 'master' file available, and waits for this server to tell it where and who to download from. This central sever (called a tracker) tells your client that 20 other people are downloading, and all have different parts of the same file. So it tells you to download a little piece from person (a), a little peice from (b), a bit from (c), etc. So this huge 100MB file that may topple on single server is now split between lots of people....