고개를 숙여요 · 고개를 숙였어요
to bow one's head; to apologize humbly, to admit defeat
Example
그는 실수를 인정하고 사람들 앞에서 고개를 숙였어요.
He admitted his mistake and bowed his head in front of everyone.
Word parts
숙이다 = to lower or bend; bowing the head shows apology, respect or defeat.