Typically when you need to completely remove a chain from your bike for thorough cleaning or whatever, you have to break the chain to get it off. Using a special tool, you destroy one of the links, and then the chain can be removed. This whole concept is painful to me.
That's what a master link is such a great thing. It's an itty-bitty part, but still probably my favorite piece on the whole bike. The master link is a single removable link segment of the chain. It is not permanently fused, which allows you to remove your chain at will, taking it off and putting it back on when needed. A master link can either be installed with a new chain, or else used as a replacement piece when putting your current chain back on after you've had to break a link to remove it as described above.
A master link looks basically like your normal segment of chain link, except that one side has a flat washer that mimics the normal side piece of the link and next that, to a removeable link-shaped clip that slides on and off, usually with the help of a screwdriver, when mounting or removing the masterlink.
Master links are cheap, too, usually only $3-4 bucks depending on where you get them.