It means that someone is passing off all responsibility or connections to an event or person. I believe the origin is from Pontius Pilate in the Christian New Testament. "When Pilate saw that he was getting nowhere, but that instead an uproar was starting, he took water and washed his hands in front of the crowd. "I am innocent of this man's blood," he said. "It is your responsibility!" Hope that helps!

To "wash your hands of something" means you don't want to take responsibility for the consequences of a decision. It means that whatever happens as a result, if it goes wrong or right, you don't want to be associated with it.

Lets say that people are doing something very bad. You don't do anything bad yourself, but you don't try to stop it. Someone might accuse you by saying "Your hands are not clean in this matter," or if it is very bad and someone may die, "you have blood on your hands." Now, let's say you do try to stop it. You try your best. You can't stop it. You give up. You say "I wash my hands of this matter." It means "I tried. I failed. I give up. It's not my fault. Don't blame me."