Both people (the two of them); indicates that each of the two persons shares the same state or action.
二人とも元気そうだね。
Both of them look well.
パーティーには二人とも来られないと言っていた。
They both said they couldn't come to the party.
二人とも留学経験があるから、英語が上手だ。
Both of them have studied abroad, so they're good at English.
先生は二人とも賞を与えた。
The teacher gave awards to both of them.