God commands in Exodus that the priests must wash their hands and their feet before entering the tent of meeting to eat the holy food. Exodus 30:18 The Mishnah and Talmud extend this to everyone that would lead a holy life, and to washing after a meal as well. A modern exposition of Talmudic reasoning says:
A certain spiritual peril lurks in any meal that we eat. Our involvement in gastronomic pleasures inevitably increases the value we assign to such activities, and decreases the importance of spiritual activities, efforts that truly perfect us. As a preventative measure, the Sages decreed that we should wash our hands before eating. Performing his ritual impresses upon us the imagery that we are like the priests, eating holy bread baked from terumah offerings. The physical meal we are about to partake suddenly takes on a spiritual dimension.The "salt of Sodom" is metaphorical. Ezekiel said: "Behold, this was the guilt of your sister Sodom: she and her daughters had pride, excess of food, and prosperous ease, but did not aid the poor and needy." Ezekiel 16:49
Despite this preparation, our involvement in the physical act of eating will reduce our sense of holiness to some degree. To counteract this negative influence, we wash our hands after the meal. With this ritual cleansing, we wash away the salt of Sodom, the residue of selfish preoccupation in sensual pleasures. This dangerous salt, which can blind our eyes to the needs of others, is rendered harmless through the purifying ritual of mayim acharonim.