Apology (noun)

1. An expression of remorse for having caused trouble or offence.
2. A defense or justification of one's actions or beliefs.

Origin:

From the greek word "apologia" meaning "a defense".

Examples:

1. He offered an apology for his behavior.
2. She made an apology for being late.
3. The company issued an apology for the mistake.
4. He made an apology for his mistake.
5. She wrote an apology letter to her friend.