I’m very glad that you asked this question, this is actually one of my favorite celebrations. What is taking place is a celebration called “Inviting the Holy Spirit”, during the Rasa Holy Qurbana of the Syro Malabar Church. Rasa Qurbana is the equivalent of the most high or exalted form or the Latin Mass. Rasa requires a minimum of three preists, one as the celebrant and two as the con-celebrants, sometimes theres even four priests like in the pictures above.
When the priests invite the Holy Spirit or in Syriac, the “Rooha”, the main celebrant and one con-celebrant step down into the middle aisle of the church and lay an anaphoral veil on the floor above a plain cloth, the other two con-celebrants remain at the altar or the altar steps. Then the hymns begin, the main priest according to the verse of the hymn, kneels before one side of the veil and prostrates, kissing the veil thrice or touching his forehead to it, and when returning into kneeling position, he raises his arms up calling upon the Holy Spirit.
As the hymn continues the celebrant continues this but around all four corners of the veil, when the celebrant returns to the original corner the con-celbrants step down from the altar and all take one corner of the veil. As the last verse of the hymn is sung they all prostrate together, making one union with the Holy Spirit (sometimes deacons and altar boys prostrate with them). When all four return to the kneeling position they remain kneeled and recite prayers before the veil. After the prayers are recited they return to the altar and continue the Holy Qurbana.