understanding
/ˌʌndɚˈstændɪŋ/
noun
the knowledge and ability to judge a particular situation or subject - usually + of; [singular]
[singular] :an informal agreement
[noncount] :a willingness to understand people's behavior and forgive them
[singular] :your belief about something based on what you have heard, read, etc.
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
adjective
[more ~; most ~] :showing sympathy and kindness :tolerant or sympathetic