A band is a metal ring that fits around the tooth. It will have a brace welded to it and is held onto the tooth with dental cement. Bands are only used on back teeth, because they do not look very attractive with all that metal showing. In years past, all of the teeth had bands on them which is where the term “metal mouth” originates. But with the invention of bonding (gluing) a brace directly onto the tooth, you do not have to use bands on the front teeth anymore.
Holding a brace onto a tooth with a band is much more durable than bonding it directly onto the tooth. This durability is very important when you have people exerting hundreds of pounds of pressure to their teeth when they chew. They can easily break a bonded brace loose from a tooth, but not a banded one. This is why bands are still used today and why orthodontists ask their patients not to chew hard or crunchy food.