If you mention something, you say something about it, usually briefly.

A mention is a reference to something or someone.

If someone is mentioned in writing, a reference is made to them by name, often to criticize or praise something that they have done.

If someone is mentioned as a candidate for something such as a job, it is suggested that they might become a candidate.

A special or honourable mention is formal praise that is given for an achievement that is very good, although not usually the best of its kind.

People sometimes say 'don't mention it' as a polite reply to someone who has just thanked them for doing something.

You use not to mention when you want to add extra information which emphasizes the point that you are making.