Your helmet should fit snugly without squeezing your head. If your helmet feels loose when you shake your head, it's too big. Most helmets are adjustable and use Boa dials, sliders, or pads to ensure a good fit. Measure your head and use the manufacturer's size chart to get the best fit.
Most helmets feature an outer ABS plastic shell lined with 'hard' EPS foam, and feature either in-mold or injection-molded construction. These helmets are designed to absorb the impact from a single catastrophic event, after which they should be discarded. A few manufacturers (like Bern) offer helmets that are lined with a 'soft' foam that's useful for multiple low-intensity hits, but these aren't rated to the same safety standard.
Most helmets, aside from perhaps skate-style park helmets, feature some kind of venting to keep your head cool and comfortable. Venting systems vary, but usually consist of outlets that allow hot air to escape and inlets that allow cooler air to enter. Often venting can be controlled with sliders or with drop-in plugs.
If you like listening to music when you ride, or simply want hands-free convenience on phone calls, look for ear flaps or attachments that add audio capabilities to your helmet. Some helmets come with audio already built in, while others are simply audio-compatible, with speaker units available separately.