apology

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun An acknowledgment expressing regret or asking pardon for a fault or offense.
• noun A formal justification or defense.
• noun An explanation or excuse.
• noun An inferior substitute.

from The Century Dictionary.

• noun Something said or written in defense, vindication, or excuse; specifically, a defense or justification of a doctrine, system, course of conduct, etc., against objections or criticisms.
• noun An excuse, usually accompanied by an expression of regret, for some fault.
• noun That which imperfectly serves a given purpose; a temporary substitute; a makeshift.
• noun An apologue.
• noun Synonyms

from the GNU version of the Collaborative International Dictionary of English.

• intransitive verb obsolete To offer an apology.
• noun Something said or written in defense or justification of what appears to others wrong, or of what may be liable to disapprobation; justification.
• noun An acknowledgment intended as an atonement for some improper or injurious remark or act; an admission to another of a wrong or discourtesy done him, accompanied by an expression of regret.
• noun Anything provided as a substitute; a makeshift.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun An expression of remorse or regret for having said or done something that harmed another: an instance of apologizing (saying that one is sorry).
• noun A formal justification, defence.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a poor example
• noun an expression of regret at having caused trouble for someone
• noun a formal written defense of something you believe in strongly