A band is a narrow strip of fabric or some other material, like the head band a little girl wears in her hair. When a patient is admitted to a hospital, she gets a plastic wrist band with her name on it.
There are many different kinds of bands, from rubber bands to wedding bands — what they have in common is being thin and flat, and forming a kind of loop or circle. Other ways to use the word band include to mean musicians who play together or another group with something in common, like a band of thieves. When you band together with others, you join them in a clump or support a common cause.