apologize
To say you are sorry for something you did wrong.
To apologize means to tell someone you're sorry for something you did wrong or for causing harm. When you apologize, you acknowledge your mistake and express regret. If you accidentally knock over your friend's carefully built tower of blocks, you might apologize by saying, “I'm so sorry! I didn't see it there.”
A sincere apology involves understanding why what you did was wrong and genuinely wishing you hadn't done it. It requires actually meaning the words you say. Compare “Sorry” muttered while rolling your eyes with “I'm really sorry I interrupted you during your presentation. I should have waited for you to finish.” The second apology shows real understanding.
Sometimes people apologize even when something isn't entirely their fault, simply because they care about the other person's feelings. If your team loses a game and you say, “I'm sorry we lost,” you're expressing sympathy, not necessarily taking blame.
The related noun is apology. A good apology often includes three parts: admitting what you did, explaining that you understand why it was wrong, and saying what you'll do differently next time. When you make a genuine apology, you're taking responsibility and trying to repair the relationship with the person you hurt.