What is BitTorrent?
BitTorrent (often abbreviated to 'BT') is a protocol (a set of rules and description of how to do things) allowing you to download files quickly by allowing people downloading the file to upload (distribute) parts of it at the same time. BitTorrent is often used for distribution of very large files, very popular files and files available for free, as it is a lot cheaper, faster and more efficient to distribute files using BitTorrent than a regular download.
What is a torrent?
A torrent is a file that is used by a program called a bittorrent client, which then uses the file to download the actual file you want. Basically, it's the middleman of the download process. You don't really need him, but still he remains.