Both is a determiner, pronoun and conjunction used to refer to two people or things together.
Common usages of both:
1. Both + noun: "I like both colors."
2. Both of + pronoun: "Both of them are students."
3. Both...and...: "She is both smart and beautiful."
4. With verbs: "They both went to the party."
5. In short answers: "Are you tired?" "Both!" (meaning both tired and not tired)