Halacha requires washing one's hands each morning, and the Rosh explains that this is because the hands move around during the night, and likely touched an unclean part of the body. According to this explanation of the Rosh, we easily understand why Halacha requires washing only the hands, and not other parts of the body.
Other sources, however, give other reasons for this obligation. The Zohar teaches that when one's soul departs as he falls asleep, he is overcome by harmful spiritual forces. Although these impurities leave when a person wakes up, they remain on the hands, and must therefore be eliminated through washing. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in the introduction to Parashat Toledot, explains that the fingers and toes are especially susceptible to the harmful spiritual forces. A person's ten fingers and ten toes, the Ben Ish Hai writes, correspond to the five Hebrew letters known as "Mansepach" – Mem, Nun, Sadi, Peh and Chaf – which are formed differently when they appear at the end of a word, for a total of ten letters. According to the teachings of Kabbalah, these letters are associated with the forces of impurity. The combined value of these letters in Gematria is 280 – the Gematria of "Par," a term which alludes to the harmful spiritual energies. Although these forces cannot descend upon a person while he is awake, they are able to cling to his fingers and toes when he sleeps. We therefore eliminate these forces with water, which represents the divine attribute of kindness that defeats the harmful spiritual energies. (The word "Mayim" – "water" – may be read as an acrostic representing the phrase "Maleh Yadenu Mi'birchotecha" – "Fill our hands with Your blessings.")
If so, then we should expect Halacha to require washing both the hands and feet each morning. Why do we wash only the hands?
Citing the Yefeh Sha'a, the Ben Ish Hai answered that these forces cannot be removed from the toes. They cling so tightly to the toes that washing is incapable of eliminating them. Only the Kohanim, who washed with the sacred water of the Kiyor in the Bet Ha'mikdash, had the ability to remove this impurity from their toes, which is why the Torah requires the Kohanim to wash both their hands and their feet before entering the Bet Ha'mikdash to perform the service. We, however, are unable to remove the impurity from our toes, and so we do not wash our feet in the morning. The Ben Ish Hai adds that the sanctity of Shabbat empowers us to remove some degree of this impurity by washing our feet on Friday in honor of Shabbat.
As we saw in a previous installment, the Rashba gave a different reason for the morning hand-washing, explaining that as we prepare to start our day of devoted service to Hashem, we resemble the Kohanim arriving at the Bet Ha'mikdash to serve. Therefore, we wash our hands each morning just as the Kohanim washed their hands and feet before serving in the Mikdash. It is unclear why, according to the Rashba, we are required in the morning to wash only our hands, and not our feet like the Kohanim.