Okay. First of all, I'll correct your question, if you don't mind (sorry, such a stupid habit of mine:) ):
Выражение "умывать руки" - можете (or Не могли бы вы)дать мне несколько примеРОВ его использования в переносном смысле?
As Ted has mentioned, it goes back to the New Testament. According to it, Pontius Pilate has tried to convince the crowd that Jesus is innocent of any crime, yet they kept demanding his execution. Finally, Pilate realized that his attempts were futile. He felt guilty about letting an innocent man die, but he was also afraid to clear Jesus of all charges (unless somebody else did it for him), because he knew his enemies might use it against him. So, he symbolically 'washed his hands', refusing to take responsibility for Jesus's death, since he couldn't prevent it, as the crowd kept shouting "Crucify him! His blood will be upon us and our children!"
It became an idiom ever since. Literally meaning "I GIVE IT UP, BUT IT"S ON YOU!"
Я УМЫВАЮ РУКИ! ПОСТУПАЙ КАК ЗНАЕШЬ, НО С ЭТОГО МОМЕНТА ВСЯ ОТВЕТСТВЕННОСТЬ НА ТЕБЕ!
I GIVE IT UP! DO WHAT YOU WANT, BUT FROM THIS MOMENT IT'S ON YOU!