2 You have seen then the Deacon who gives to the Priest water to wash, and to the Presbyters who stand round God's altar. He gave it not at all because of bodily defilement; it is not that; for we did not enter the Church at first with defiled bodies. But the washing of hands is a symbol that you ought to be pure from all sinful and unlawful deeds; for since the hands are a symbol of action, by washing them, it is evident, we represent the purity and blamelessness of our conduct. Did you not hear the blessed David opening this very mystery, and saying, I will wash my hands in innocency, and so will compass Your Altar, O Lord? The washing therefore of hands is a symbol of immunity from sin.
Source: Catechetical Lectures (New Advent)