To banish is to get rid of. Think very carefully before you banish someone from your group. Someday, you may want that person around again.
Banish rhymes with vanish, which is exactly what happens when you banish someone. Suppose a king, angry with some of his subjects, banishes them. They have to leave the kingdom and vanish — not just go home and wait for the king to change his mind. Banish comes from the Old French word banir, which means “proclaim as an outlaw.” It is serious and absolute. You can see the word ban in banish, but to ban something is not as harsh as banishing it.