From MopedWiki

A helmet or lid is a form of protective clothing worn on the head and usually made of a hard substance, such as Kevlar, resin fiber, or plastic. Worn for protection of the head in case of an accident. Most state laws require that you wear one. Typical styles include half (ears exposed), 3/4 (ears covered), and full-face (entire head protected).

A good article on motorcycle helmets, DOT vs. SNELL ratings, some helmet reviews, common crash scenarios, and other information to chew on. Also see this webpage for a diagram that shows the distribution of impact locations on motorcycle helmets. Note that the highest percentages are on areas of your head not covered by a half or 3/4 helmet.

Make sure to watch this YouTube video before you decide to ride without a helmet.