1un·der·stand·ing 
/ˌʌndɚˈstændɪŋ/ noun
/ˌʌndɚˈstændɪŋ/ noun 1 : the knowledge and ability to judge a particular situation or subject — usually + of [singular] ▪ He has a thorough/full understanding of the subject. ▪ She has a basic/better/deep understanding of the process. ▪ I hope to get/gain a clearer understanding of the issues involved. [noncount] ▪ He seems to have little understanding of our situation. 2 [singular] : an informal agreement
▪ We have an understanding that whoever cooks doesn't have to do the dishes. ▪ After a long discussion they finally achieved/reached an understanding. = After a long discussion they finally came to an understanding. [=they finally agreed] 3 [noncount] : a willingness to understand people's behavior and forgive them
▪ She treats them with kindness and understanding. ▪ a relationship based on mutual understanding 4 [singular] : your belief about something based on what you have heard, read, etc.
▪ My understanding was that you were going to help. = It was my understanding that you were going to help. [=I thought that you were going to help]
▪ We have an understanding that whoever cooks doesn't have to do the dishes. ▪ After a long discussion they finally achieved/reached an understanding. = After a long discussion they finally came to an understanding. [=they finally agreed]
▪ She treats them with kindness and understanding. ▪ a relationship based on mutual understanding
▪ My understanding was that you were going to help. = It was my understanding that you were going to help. [=I thought that you were going to help]
on the understanding that
— used to say that something is done, accepted, etc., because you have been told that something else will happen or is true ▪ She agreed to do the work on the understanding that she would be paid now.
