Some people are under the impression that the humeral veil is worn to stop unconsecrated hands from touching consecrated objects. However, this is untrue. As I have explained before, only consecrated things may touch the Eucharist itself, but there need not be an infinite regress of consecrations to touch consecrated things.
In fact, touching consecrated vessels used to be limited simply to clerics in Major Orders and was one of their distinguishing priveleges that made them Major rather than Minor (even though the subdiaconate is a sacramental and not a Sacrament proper). Yet the subdeacon uses the humeral veil to hold the paten during Solemn Mass, even though during his ordination he is handed an empty paten and chalice (thus showing he can touch consecrated vessels without issue).
Rather, the humeral veil (note similarity of the term "humeral" to "humility") seems to signify that the object one is holding does not belong to you. So, for example, in Benediction. The priest holds the monstrance with a humeral veil. Now, monstrances are not consecrated (only the luna, the "clip" which holds the Sacred Host, is consecrated). But the priest covers his hands and arms with the humeral veil so that it is clear in Benediction that it is Christ in the Blessed Sacrament who blesses, not the priest. The priest "disappears" (his face may even be covered by the monstrance itself if it's big enough and you look straight-on).
A similar principle is true for the so-called vimpa. The vimpa is a shawl worn by servers at Pontifical Masses to hold the mitre and crosier, to show that they do not belong to them (they are proper to the bishop himself, of course). However, the distinction between vimpa and humeral veil seems rather late, and even Catholic Encyclopedia in 1917 seems to indicate that the vimpa is just a humeral veil (if made smaller in size), as it speaks of the "humeral veil worn by the mitre-bearer" which I'm pretty sure means what is often now called the vimpa in traditionalist circles. Green vimpae for the mitre and crosier are shown here:
The vimpae below illustrate this principle of showing to whom the items are actually proper quite nicely by having on their backs the Arms of the Cardinal whose mitre and crosier they are bearing, indicating that they are to be associated with him and not the servers themselves:
Here is a familiar face as subdeacon bearing the paten in humeral veil at a Solemn Mass:
Why the humeral veil for subdeacons with the paten at Solemn Mass like this? The same Catholic Encyclopedia article seems to suggest that originally the paten was borne by an acolyte and was not held by the subdeacon until later. This would explain the humeral veil and hark back somewhat to the theory that the humeral veil is about people holding (consecrated) vessels they shouldn't touch. The subdeacon apparently bore the chalice with a cloth that later evolved into the chalice veil.
However, I'd also theorize that it may be related to the concept of the humeral veil signifying non-ownership of a held item in liturgy too. While subdeacons can touch patens and other consecrated vessels (say, during distribution of communion, as no "stick" is required for paten for a subdeacon, or for washing in the sacristy, etc)...the paten at Mass might be seen as "proper" to the priest and thus belonging only to him (so when a lesser minister bears it, he wears the humeral veil.)
Even more interesting, I might theorize it perhaps relates to the origin of the rite of the comingling, the so called fermentum, as explained in this book:
The unity of the local church with its bishop celebrated in the stational liturgy was especially evident in the ancient practice called the fermentum (literally 'leaven'). Roman presbyters were obliged to celebrate the Eucharist on Sundays and feast days in their own churches (tituli) for those who could not take part in the solemn papal Eucharist. As a symbol of the communion shared between the Bishop of Rome and his flock--present and absent--the bishop broke off small pieces of his host at the time of Communion which would be given to each of the tituli for their own Eucharist that day. The small piece of that host was then carried by the acolytes or deacons back to those churches. At the moment of Communion, the presbyters would place the small fragment of the papal host in the chalice. Pope Innocent I attests to the practice in a famous letter sent to Decentius, Bishop of Gubbio, in the year 415. It is not clear when the custom was introduced, and after the seventh century, with the waning of the stational liturgy, it was only continued at the Easter vigil.Perhaps the holding of the paten in a humeral veil by acolytes and later subdeacon evolved from the bringing of the fragment of the fermentum from the papal liturgy to the various tituli. One can imagine that a minister would hold this paten with the papal fragment (which did not belong to them, but to the Pope) until it was time for the comingling (whose origin is certainly in this practice of the fermentum). At least, that's what I always imagine the historical provenance is when I'm at a Solemn Mass.