When you're cuddled up with your furball, you may notice that he gets to purring when you start rubbing under his chin. It's natural to be curious about this as a new cat owner --- cats are sometimes peculiar yet very lovable creatures. A cat might like his chin rubbed for one of a couple of logical reasons.
In some cases, a cat likes his chin rubbed because it's itchy. The itchiness is often due to acne. The chin is a common place where cats get pimples and other acne problems. It is sometimes causes by irritants to the skin, sometimes due to allergies; in some cases it is simply due to the type of food bowl the cat eats from.
If you'll notice, your cat uses his head often to rub up against you when he's content -- or wants something. Cat's do this as a way to leave their mark on you --- it is territorial. The sebaceous glands leave an oil and a corresponding scent on objects, including humans. In some cases, the cat simply likes to have his chin rubbed because it transfers his scent onto your hands. You're basically helping him to mark you as his owner.
The area under a cat's chin is often very sensitive. They may simply like the rubbing sensation, similar to running your finger nails lightly across someone's feet. When you make your cat happy it is a crucial step in the bonding process. So if you have a new cat and he seems to enjoy the chin rubbing, oblige him.
If your cat allows you to rub his chin without biting or swatting at you, that is a possible indication of trust. The chin is right in between the stomach, which cats often guard like Fort Knox, and his sharp teeth. Like all activities with your cat, don't overdo it, because it could become annoyance to him when done in excess.