A coin is a small piece of metal which is used as money.

If you coin a word or a phrase, you are the first person to say it.

If you say that someone is coining it or is coining money, you are emphasizing that they are making a lot of money very quickly, often without really earning it.

You say 'to coin a phrase' to show that you realize you are making a pun or using a cliché

You use the other side of the coin to mention a different aspect of a situation.

If you say that two things are two sides of the same coin, you mean that they are different ways of looking at or dealing with the same situation.