If you have an understanding of something, you know how it works or know what it means.

If you are understanding towards someone, you are kind and forgiving.

If you show understanding, you show that you realize how someone feels or why they did something, and are not hostile towards them.

If there is understanding between people, they are friendly towards each other and trust each other.

An understanding is an informal agreement about something.

If you say that it is your understanding that something is the case, you mean that you believe it to be the case because you have heard or read that it is.

If you agree to do something on the understanding that something else will be done, you do it because you have been told that the other thing will definitely be done.