One of the nine enactments instituted by Rabbi Yochanan ben Zakai (who lived at the time of the destruction of the Second Temple) pertains to the law of Birkat Kohanim. He decreed that the Kohanim must not ascend the duchan to bless the nation while wearing sandals or shoes. There are a number of reasons for this enactment, one being out of respect for the congregation, for it is not appropriate for the Kohanim to bless the nation with mud on their shoes. Likewise, the Temple services were performed by the Kohanim without shoes, due to the sanctity of the site. The halachic reason for this enactment is that the laces of the Kohen’s shoes might become loose, causing him to feel uncomfortable standing on the duchan, which is a high place, where he can be seen by the whole nation. To hide his embarrassment, he would have to bend down and tie his laces, and the people might misinterpret his bending and not reciting Birkat Kohanim as his admission of not actually being a Kohen (Sotah 40a).
Based on these reasons, a Kohen may not ascend the duchan with shoes or sandals, nor with slippers that have laces. Regarding slippers, if they are made of leather, even without laces, it is prohibited to ascend the duchan in them as well, since ordinary shoes are generally made of leather, and all leather shoes are included in the enactment of Rabbi Yochanan ben Zakai. However, it is permissible to ascend the duchan in non-leather slippers that do not have laces.
In a place where it is not customary to appear barefoot, or in sandals without socks, before respectable people, it is proper that the Kohanim ascend the platform with socks on their feet (Mishnah Berurah 128:18). In a place where it is customary to walk in sandals without socks, even in front of respectable people, it is permissible for Kohanim to bless the people while barefooted (Olat Tamid 128:11).
At times, the question arises: what does a handicapped Kohen do if he is unable to take off his shoes, and likewise, what does a Kohen in the army do when he does not have time to remove his army boots? In cases of extenuating circumstances like these, some poskim are lenient and allow a Kohen to bless the people while standing on the floor of the synagogue, not ascending the duchan, where, because of its elevation, their feet and shoes can be seen, and this would bring disgrace to the blessing. If however, the Kohen is standing on the ground at the same level as the congregation, there is no prohibition to recite the blessing while wearing shoes. In extenuating circumstances, the Kohanim can rely on these poskim and bless Israel on the floor in shoes, provided that their shoes are clean (see Igrot Moshe, Orach Chaim, part 2, 32, regarding a handicapped person; concerning the issue of extenuating circumstances, see Tzitz Eliezer 14:11 and Yechaveh Da’at 2:13).