He was forced to ask for their help 'on bended knee'. [=he was forced to beg for their help; he was forced to ask for their help in a very humble way]
If you want to clean the floor properly, you have to 'get down on your (hands and) knees' [=you have to kneel down on the floor] and start scrubbing.
She 'dropped/fell/sank to her knees' [=she knelt down] and begged for forgiveness. = She 'got down on her knees' and begged for forgiveness.
(..) Is that right? You and the pretty crow do a lot of talking, Tormund? And when you're done talking, do you get down on your knees and suck his cock? ( grunts ) Gather the elders and let's talk. My name's Jon Snow. (..)2015 TvShow: Game of Thrones Title: Hardhome Season: 5 Episode 8