The Torah says in this parsha that a laver will be made with a base and Ahraon and his sons will wash from it. (Chapter 30, 19).
The holy Ishbitzer comments that washing by the Kohanim is a method which their mind and body submit to the work they must do. Washing by the kohan is a personal nullification to serve Hashem fully. The Ishbitzer relates this to our lives today, regarding hand washing before eating. He says that we wash so that the intensely physical and gratifying act of eating is transformed into a spiritual submission. We wash before we eat to ensure that our physical act is sublimated to our spiritual mission. All physicality is done for the sake of the spiritual.
The Ishibitzer goes further and says the hand washing prior to eating is a form of prayer. It is a prayer that the physical benefit we derive from our food will only be for spiritual benefit. To further demonstrate this idea, the proof is that the passage of the Kohanim washing is recited daily, prior to the daily sacrifices. The sacfices are our supplication to Gd and the washing ensures that even our prayers are intended for our spiritual benefit.