It is called as Aër.
is the largest and outermost of the veils covering the Chalice and Diskos (paten) in the Eastern Orthodox Church and the Eastern Catholic Churches which follow the Byzantine Rite. It is rectangular in shape and corresponds to the veil used to cover the chalice and paten in the Latin Rite, but is larger.
There was the following in Divine Lithurgy:
Just before the chanting of the Symbol of the Faith (Nicene Creed), the Priest will kiss the Diskos and Chalice (by kissing the Aër in the place where it touches each vessel) and the front edge of the Holy Table. During the Creed, the priest will hold the Aër above the Gifts and waive it slowly, indicating the activity of the Holy Spirit. When a bishop is serving the Liturgy, the concelebrating priests will hold the Aër during the Creed as the bishop kneels (or bows his head) underneath it. After the Creed, the Aër is folded and placed on the Holy Table.
And as for the Divine Lithurgy:
this symbolizes the descent of the Holy Spirit.
The aer also represents the shroud of Christ.
A priest taking the aer from Blessed Sacraments reminds about a stone, which had been shoven off from doors to Holy Sepulcher. Furthermore, taking the aer from the Blessed Sacraments is being completed in sign of the faith opens secrets of Divine Wisdom to us.
In time singing of the Credo the priest reads it himself, then take up, and fluctuate the aer over Blessed Sacraments. This takes place in sign of the breezing over them of coming descending of Holy Ghost, like breath of the wind precedes to the descending of the Holy Ghost unto Apostles.
2 And suddenly there came a sound from heaven as of a rushing mighty wind, and it filled all the house where they were sitting. Act 2 KJV
Furthermore, taking up, and fluctuating of the aer reminds about the earthquake that took place during opening Holy Sepulcher, and about guard's run out of Holy Sepulcher. (In Russian).
2 And, behold, there was a great earthquake: for the angel of the Lord descended from heaven, and came and rolled back the stone from the door, and sat upon it. Matt 28 KJV