Lady Macbeth tells Macbeth to wash the "filthy witness" from his hands, where the "filthy witness" is the blood still on Macbeth's hands after he kills King Duncan at their castle. Macbeth hears knocking over and over again, which the audience is supposed to take as his conscience starting a slow mental decline. No matter much he washes, he is unable to wash all the blood from his hands.
Macbeth illustrates the amount of blood on his hands by saying even Neptune's ocean is unable to wash it all away. This represents the extreme guilt Macbeth is feeling from killing the king, which took place due to pressure from his wife and his own ambitions.
It is not so much the killing of the king that starts Macbeth's demise, but rather the mental deterioration and constant feeling of needing to protect himself from other potential traitors that makes Macbeth practically fear his own shadow, as well as his former friends and soldiers.
Although killing King Duncan was not easy for Macbeth, nor was it a task he wholeheartedly wanted to accomplish, this washing of the "filthy witness" opened a gruesome, ambitious and greedy door for Macbeth for the rest of the play.