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un‧der‧stand‧ing1 W3
1 [singular, uncountable] knowledge about something, based on learning or experience COLLOCATIONS COLLOCATIONS
have an understanding/some understanding of something have little/no understanding of something gain/get an understanding of something a better/greater/deeper understanding of something a clear understanding of something a thorough/proper/full understanding of something a basic understanding of something
COLLOCATIONS have an understanding/some understanding of something have little/no understanding of something gain/get an understanding of something a better/greater/deeper understanding of something a clear understanding of something a thorough/proper/full understanding of something a basic understanding of something
2 [countable usually singular] an unofficial or informal agreement
come to/reach an understanding (=stop arguing and agree) 
My father was furious at first, but eventually we came to an understanding.
My father was furious at first, but eventually we came to an understanding.3 [singular, uncountable] the ability to understand people's behaviour and to forgive them when they do something wrong : The principal listened to the boy's story with sympathy and understanding.
The principal listened to the boy's story with sympathy and understanding.4 [uncountable] the way in which someone judges the meaning of something According to my understanding of the letter, it means something quite different.
somebody's understanding (of something)
According to my understanding of the letter, it means something quite different.5 if you agree to something on the understanding that something else will be done, you agree to it, believing that it will be done : Jack lent Sarah the money on the understanding that she would pay it back next month.
on the understanding that
Jack lent Sarah the money on the understanding that she would pay it back next month.