First, we must note that a priest is ordained to bless and consecrate the people of God with his hands, that is why one without hands cannot be ordained, he’s said to have a canonical impediment. Thus, the hands of the priest are consecrated at Ordination.
Apart from blessing the people of God, there’s a special moment reserved for Christ Himself to bless his people. This moment is called *Benediction of the Blessed Sacrament*
During the Benediction of the Blessed Sacrament (as it is called) “the Blessing of Christ”, it is not the priest who blesses or acts, neither does he act or blesses in the person of Christ, no, it is Christ himself (the true Priest) who acts and blesses at that very moment He’s exposed on the altar. Therefore, in order to illustrate that the priest is not blessing the people, he covers (hides) his hands (used for blessing) with a humeral veil (humurus means “shoulder” so a humeral veil is a “should veil”).
Thus, once the hands of the priests isn’t seen, it would be understood that he’s not the one blessing the people but Christ himself.
Therefore, at benediction, adoration, or during the procession of “Corpus Christi” (an offshoot of benediction), the priest carries the Blessed Sacrament in procession with his hands hidden, while the blessings of Christ continue to radiate in all its rays towards the people (as seen in the shape of the monstrance). It is Christ himself who goes about in procession.
Source: Catechism of the Catholic church