After a long discussion they finally 'achieved/reached an understanding'. = After a long discussion they finally 'came to an understanding'. [=they finally agreed]
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]
She agreed to do the work 'on the understanding that' she would be paid now.
(..) How...? Why would you make a deal with that scumbag? - You see what he did to me? - Because I think... ...that we can do business together. We came to an understanding. No way, man. Okay? No understanding. Take a look at the money in your hand. Now, just imagine (..)2008 TvShow: Breaking Bad Title: A No-Rough-Stuff-Type Deal Season: 1 Episode 7