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.
(..) for a while. And then they want the angry little kid to do something he knows he can't do. Move on. So, after a while, they stop understanding. They send the angry kid to a boys' home. I figured it out too late. You gotta learn to hide the anger. Practice smiling in a mirror. (..)2012 The Dark Knight Rises