This is the 1954th most frequent Korean word.
동의
Agreement; consent.
Here, '동의합니다' ('동의하다' verb in polite form) means to agree with a certain point or perspective, indicating concordance with someone's stance or thought.
나는 당신의 의견에 동의합니다.
I agree with your opinion.
In this usage, '동의 서명' combines '동의' with '서명' (signature), referring to the act of agreeing formally by signing a document.
이 문서에 동의 서명을 해주세요.
Please sign this document to indicate your agreement.
The phrase '동의를 표했다' (expressed agreement) uses '동의' as a noun combined with '표하다', indicating actively showing or stating agreement concerning a proposal.