The priestly blessing is one of the main features of this portion (Num. 6:23-27). It is recited by the kohanim with their shoes removed. This reflects the practice in the Temple, where the priests ministered barefoot.
However, the Mishnah B’rurah (128:18) explains that going barefoot today is regarded as improper, though there is no objection to saying the blessing in socks. Some synagogues have non-leather slippers available for the kohanim (at the Great Synagogue, Sydney, we provided airline slippers by courtesy of a member of the congregation who was an airline executive).
The rationale behind not wearing normal shoes for the priestly blessing is partly that this reminds us that the angels in heaven who minister to the Almighty do not need earthly creature-comforts, and everyone, especially the kohen, should aspire to emulate the heavenly hosts.
It also teaches us that it is when people are uncomfortable that they particularly need God’s support and blessing, and when people are comfortable they need to think of how they can help and sustain others who may not be so fortunate.