Wearing a helmet increases your maximum HP by +1. This applies regardless of what other armor (or lack of armor) you are wearing.
A helmet must be something that both appears to be an in-decorum piece of headgear and is also capable of protecting your head from hard blows. If you intend to wear a helmet, you must bring it to weapons-check to ensure that it provides enough protection. If it isn’t padded enough, it will be disqualified and you will not be allowed to wear it into combat. The reasoning here is that if you are wearing a helmet that doesn’t offer proper protection, your opponents in a fight may mistakenly hit you too hard, creating a potentially serious safety hazard in the chaos of combat.