A simple explination
When you sign the guestbook, this site stores your name, your message, and a scrambled ("hashed") version of your IP address. It's used for one thing only: stopping spam and repeat abuse.
Let's be honest, are you comfortable with anyone having your full IP?
A hash is a one-way scrambling process. Your IP goes in, a fixed-length jumble of letters and numbers and symbols which the site owner (me) created by repeatedly mashing my keyboard, and then it bakes out a hashed ip.
Imagine your IP as a steak. I present to you: a RAW steak. "The fuck is this?" you exclaim. "It's your IP sir." (not hashed, not protected, can view your actual IP). "Are you a fucking idiot? IT'S RAW DAMN IT. MAKE ME A NEW STEAK!". I kindly take the raw steak and cook it. "I present the steak sir." (hashed, no one can see your IP.) Everyones happy, you have your steak, and I can stop spam.
Nobody see's your IP. You can rest easy now.