BitTorrent (often abbreviated to 'BT') is a protocol that allows you to download files quickly and efficiently. It is a peer to peer protocol, which means you download and upload to other people downloading the same file. BitTorrent is often used for distribution of large files or popular content as it is a cheap, fast, efficient way to distribute files to users like you.
µTorrent is a BitTorrent client, so it speaks the BitTorrent protocol, much like a browser would speak HTTP. Just as there are multiple web browsers, there are multiple BitTorrent clients, and µTorrent is the most popular.
Watch an introduction video below: