BIND is a server that allows remote users to turn network names into IP numbers.
eg) foo.mydomain.com => 10.0.0.1
I use BIND so that I may have a do-it-yourself domain. If you are also experimenting with hosting a domain yourself you will need BIND too. However BIND has many known security problems and is rather complex. It's important that you know what you are doing when you secure your name server. Here's a link to O'Reilly's book on bind.