The promise is applied to the public prayer of the congregation, as we see in what is called "the prayer of St. Chrysostom" in the English Prayer book. Are gathered together. For the purpose of worship.
It is a simpler form of the word used in Hebrews 10:25, "Not forsaking the assembling of ourselves together." In my Name ( εἰς το Ì ἐμο Ìν ὀ ìνομα); literally, into my Name; i.e. with love to me, yearning for union with me, and acting for my glory.
This would imply decent and orderly meeting for the highest ends. There am I in the midst of them. Christ promises a real, actual presence, though invisible, as true as when he appeared to his disciples after his resurrection, as true as when the Shechinah shone in tabernacle or temple.
The rabbis had a saying that if two sat at table and conversed about the Law of God, the Shechinah rested upon them. The promise in the text, of course, implies Christ's omnipresence and omniscience.
This is his blessing on united, congregational prayer.