I suppose that every day, somewhere in the world, a solemn High Mass is said. It is supposed to be the norm rather than the exception, but the average parish will only have a priest with no one to function as Deacon or Subdeacon. I once tried to argue the case in the CofE that the office of Reader ought to be converted into that of Subdeacon, but the lack of interparish cohesion rather put the mockers on that idea.
The office of Subdeacon is practically extinct in itself. At High Mass, the liturgical role of Subdeacon is taken by a Deacon or Priest. The Liturgical role of Subdeacon is, like the other sacred ministers, packed with symbolism and meaning. (And, yes, I'm fully expecting to be accused of pushing the symbolism again. I make no apologies.)
Functionally, the Subdeacon is the Deacon's deacon. His job is to be by the Deacon's side when the Deacon plays his part, holding the Gospel for him, passing things across, and standing behind him during the prayers.
It is at the Offertory when the role takes on its unique character, thanks to the humeral veil.
The veil itself should cover the credence at the beginning of High Mass. In this we see that it represents the Veil of Mystery that is uncovered in the Apocalypse. God reveals Truth to us by taking the veil away. The drama of the sacrifice of the Mass is that revelation.
The Subdeacon, then, as the sole bearer of the humeral veil takes upon the role of the vehicle of God's revelation. First, he reveals the chalice and paten at the Offertory which are taken by the Deacon to be presented to the Celebrant.
In this we essentially see the Lord's prophecy of His Death being revealed. The Chalice will become a symbol of God's covenant with us in which humanity and divinity are mixed and together become the Blood of Christ. The Paten becomes the Tomb on which the broken Body of Christ is laid. At the Offertory, this is a time of prophecy; the hour has not yet come. Thus, the Deacon returns the paten back to the Subdeacon under the veil, and the Subdeacon retires behind the Sacrifice until the hour indeed has come and the Broken Body of Christ is to lie before its resurrection in all who consume it in faith.
Further, it is the Subdeacon who distributes the Pax to the clergy in choir. Why the Subdeacon and not the Deacon? The Celebrant prepares himself to receive Christ into Himself. With the Deacon on side to help in this moment, the Subdeacon must bear the responsibility of bringing the Peace of Christ to the clergy and thus out into the world. Again, the Subdeacon is an agent of revelation and proclamation.
The loss of the Subdiaconate to the Church is unfortunate, and perhaps telling of this age's hatred of Mystery. All of Reality bears mysteries that cannot readily be solved. Yet one can understand a mystery, but not br able to communicate it. Words are not enough to explain all truth and only a life which recognises the Cosmic Humeral Veil in humility and faith may be permitted by the Divine to peek beneath it.