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.
(..) Captain... if I can convince the owner of the pharmacy to drop his complaints against Dr. Thackery... ...will this sufficiently satisfy your understanding of the letter and the spirit of the law? Breaking and entering carries with it a minimum sentence of five years at Sing Sing. (..)2014 TvShow: The Knick Title: The Golden Lotus Season: 1 Episode 9