1to apologize — to express regret or say sorry for a mistake or offense.
遅刻したので彼に謝った。
I apologized to him because I was late.
まずはきちんと謝ることが大切だ。
First, properly apologizing is important.
彼女は誤解を招いたことについて深く謝った。
She apologized deeply for causing the misunderstanding.
2(dated) to refuse or decline — an old usage where 謝る meant to turn down an offer or invitation. Essentially unused in modern Japanese.
3(dated) to be unable to bear; to be defeated or at a loss — an archaic meaning essentially unused in contemporary Japanese.