Gemara: Rav Yehuda said in the name of Rav: The following is the custom of Rabbi Yehuda bar Rabbi Ila’i: On Friday, they would bring him a trough full of hot water and he would wash his face, hands, and feet. He would cover himself and sit in a cloak made of linen with tzitzit, and he would resemble an angel of Hashem Tzevakot.
Ein Ayah: The sacred and the mundane are separated one from the other by their very nature. The mundane and all the actions that surround it are that which prepare life to be able to reach its goal. It gives the material world the strength and the preparation so that it can be raised to its real purpose – matters of sanctity.
Matters of sanctity are the goal of life. One reaches this goal when his godly soul is in a perfect state of tranquility. A person is in his greatest glory at the time when his spirituality is strongest. Then he is aware that he is living a life of truth, in which he is able to experience the pleasantness of Hashem and relish the aura of His glory.
For the great majority of people, the days of the week are dedicated to mundane needs, and thoughts of these needs along with physical desires take over their whole persona. Therefore, when the holy day of Shabbat arrives, they need to raise themselves up from the "valley of the lowly" mundane life and wash themselves from the swamp of materialism so that they will merit receiving spiritual enjoyment of the sacred. When successful, that which they will absorb on Shabbat will also give fruit during the coming week.
The situation is different for a person who is sacred to Hashem – a truly pious individual who makes his Maker proud, who is so holy that he is engulfed in sanctity throughout the week as well. Even those of his needs and activities that we would normally consider mundane are performed with total purity, with the internal side of the heart ablaze with an everlasting holy flame of love of Hashem and the light of His Torah. When Shabbat comes, there is a change toward additional sanctity, but it is for the most part just a more visible display of sanctity in the eyes of normal beholders. The contrast is that during the week the "cloak" of mundane activities and the external involvement in various needs covers the divine light that is the holy person’s spirit, so that it cannot be perceived in all its glow and splendor. [Internally, there is little change.]
Rabbi Yehuda bar Rabbi Ila’i was a pious man of historic proportions. Therefore, when washing himself [an act that characterizes purification and not just removing physical dirt], he washed only external parts of his body (face, hands, and feet), which can sometimes be seen. In other words, his cleansing was in relation to the external parts of his life, in which there could be a perception that there was a major distinction between his sacred and his mundane life. However, regarding his essence [represented by his body], there was no distinction between holy and mundane, as all his bones were always in a state of joy in their connection to the Holy of Israel.
He would have a trough filled to the top with hot water, so that it would be clear that there was enough water to clean his whole body, yet that he chose not to. This was to teach his associates with the potential to follow in his spiritual footsteps that they should get used to elevating themselves to the point that their internal elements would remain in a constant state of full Shabbat, tranquility, sanctity, and honor. The washing should remain active in regard to that which represents the external part of his being. In that realm there is still a difference between weekday and Shabbat to the extent that one has to raise himself to a higher level of purity so that even his external side will be prepared for Shabbat.