Short answer: read the FAQ.
A needlessly long and serious answer -- it's basically a pseudo-account system. Anyone on 4chan can pick any name they want, so a name alone doesn't identify a user. However, a name + password combination does. You can input "name##password" into the name field, and the ##password part (called a "tripcode") will turn into a hashed value of your password -- always the same value as long as the same password is used. It can be useful if you want to maintain a persistent identity and avoid someone impersonating you, however, it's not commonly used here, and, if you couldn't tell from the name, pretty much frowned upon -- this is the internet, nobody gives a fuck about your identity.
