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.
(..) I'll be back after the dinner rush. But I've got a family situation. So you'd like to take off, go home, take care of business? Thank you, Martin, for understanding. Well, don't thank me, because the answer is no. All right, Martin. What part of "family situation" do you not understand? (..)1998 TvShow: Charmed Title: The Truth Is Out There... and It Hurts Season: 1 Episode 8