Not every jewish knows what is mayim achronim, depends on  how religious his family is. At the conclusion of a meal in which we have eaten bread, we say the Grace after Meals, thanking G‑d for giving us sustenance. Before reciting the Grace after Meals, we rinse our fingertips. This washing is called Mayim Achronim, “final waters” (as opposed to Mayim Rishonim, “first waters,” which refers to the required hand washing before consuming bread).
During the course of a meal, it is highly likely that the hands become dirtied. The primary reason for Mayim Achronim is our desire to have clean hands when uttering G‑d’s name in the blessing we are about to recite. This is comparable to the services that were held in ancient times in the Holy Temple of Jerusalem when a priest was required to wash and purify his hands before serving in the Temple.
Another reason for Mayim Achronim is to wash off any “Sodomite salt” (a type of fine salt used in Talmudic times) which may remain on the fingers. This particular salt posed a grave danger if it came in contact with the eyes. Although this concern no longer applies since this type of salt is not common today, it is still appropriate to wash our hands before mentioning G‑d’s name in the course of the Grace after Meals.
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