This ceremony is known as Urchatz, "Washing of the Hands". This is a symbolic act of purification, which precedes participation in the religious service. This comes from Psalm 24:3-4:
Who may ascent the hill of the Lord? Who may stand in his holy place? He who has clean hands and a pure heart. Psalm 24:3-4Yeshua taught us that the sign of a pure heart is the heart of a servant when he washed the feet of his disciples.
After that, he poured water into a basin and began to wash his disciples' feet, drying them with the towel that was wrapped around him. John 13:5
When he had finished washing their feet, he put on his clothes and returned to his place. "Do you understand what I have done for you?" he asked them. "You call me 'Teacher' and 'Lord,' and rightly so, for that is what I am. Now that I, your Lord and Teacher, have washed your feet, you also should wash one another's feet. I have set you an example that you should do as I have done for you. I tell you the truth, no servant is greater than his master, nor is a messenger greater than the one who sent him. Now that you know these things, you will be blessed if you do them." John 13:12-17