This is the 8507th most frequent Japanese word.
承
"承" means "to receive, to accept, to take over, or to acknowledge."
In this sentence, '承' is used as part of '承諾', which means agreement or approval, indicating a formal acceptance of conditions.
この契約書に署名することで、条件を承諾します。
By signing this contract, you agree to the terms.
Here, '承' is part of '承知', meaning being aware or consent. It implies knowledge or acknowledgment of a situation.
完全に承知しておりますが、それでも挑戦してみたいです。
I'm fully aware, but I still want to try.
In this case, '承' appears in '承認', meaning approval or authorization, referring to formally granting permission for something.