Apologize (verb)

1. To express regret or remorse for something.
2. To make an apology or excuse for something.
3. To acknowledge and express remorse for a mistake or offense.

Origin:

Late 16th century (in the sense "make a defense"): via french from greek apologizesthai "speak in defense", from apo- "from" + logos "speech".

Examples:

1. I apologize for my behavior last night, I was out of line.
2. She apologized for being late, traffic was terrible.
3. He apologized for the mistake and promised it wouldn't happen again.
4. The company issued an apology for the inconvenience caused by the outage.
5. The politician apologized for the offensive remarks he made during the debate.