Alexander Boguslawski comments on some theological implications of this great icon.
Very few artists before Rublev dared to eliminate all the narrative elements from the story, leaving only the three angels; usually those who did so had to deal with limited space. The results of their efforts did not find general acceptance or many copyists. Rublev was the first to make a conscious decision not to include in his composition the figures of Abraham and Sarah because he did not set out to illustrate the story of the hospitality of Abraham, as did many painters before him, but to convey through his image the idea of the unity and indivisibility of the three persons of the Trinity.
The doctrine of the Trinity, difficult to explain logically, found various interpretations. Some thought that the Trinity consisted of God the Father, God the Son, and God the Holy Spirit. Others believed that it was just God and two angels. In the 14th and 15th-century Russia, in the period of many heretical movements, the idea of the Trinity was often questioned. The heretics in Novgorod claimed that it is not permissible to paint the Trinity on icons because Abraham did not see the Trinity but only God and two angels. Other heretics rejected the idea of the three hypostases of God altogether. The church fought the heresies with all the means it had -- usually with polemical treaties, but also with force, if necessary. Russian icon painters before Rublev subscribed to the same point of view that Abraham was visited by God (in Christ's image) and two angels. Hence, Christ was represented in icons of the Trinity as the middle angel and was symbolically set apart either by a halo with a cross, by a considerable enlargement of his figure, by widely spread wings or by a scroll in His hand.
Trinity Icons. From left to right: Holy Trinity, a part of a quadripartite icon from Novgorod (first half of the 15th c.), Holy Trinity (Hospitality of Abraham), Novgorod School (middle of the 16th c.), Holy Trinity, Pskov School (15th c.).
In Rublev's icon for the first time all the angels are equally important. Only this icon truly conforms to the Orthodox idea of the Trinity. But Rublev's genius allows the painter to go beyond the constraints of theological theme. His icon is a special kind of challenge to the antitrinitarians -- instead of forcing them to accept the dogma, Rublev softly and gently tries to bring them to the dogmatic understanding of the icon's meaning.
All scholars agree that the three hypostases of the Trinity are represented in Rublev's icon. But there are greatly differing views as to which angel represents which hypostasis. Many see Christ in the middle angel and God the Father in the left. Others see God the Father in the middle angel, and Christ in the left one. The middle angel occupies a special place in the icon: it is set apart not only by its central position, but also by a "regal" turn of its head towards the left angel, and by pointing with its hand towards the cup on the table. Both the turn of the head and the gesture are important clues to the hidden meaning of the icon. Equal among equals, the middle angel has such expressive power that one hesitates not to see in it a symbolic representation of God the Father. On the other hand one cannot fail to notice that the left angel is also essential: two other angels lower their heads towards it and seem to address it. Therefore, if we assume that the left angel is God the Father, the middle angel, dressed in the clothes customarily used in compositions depicting the second person of the Trinity (a blue himation and a crimson tunic), should represent Christ. This amazing and perhaps purposeful encoding of these two persons of the Trinity by Rublev does not give us a clear clue for a single interpretation. Whatever the case, the icon shows a dialogue between two angels: The Father turns to His Son and explains the necessity of His sacrifice, and the Son answers by agreeing with His Father's wish.
Neither of these interpretations impacts the interpretation of the Trinity as triune God and as a representation of the sacrament of the Eucharist. The cup on the table is an eucharistic symbol. In the cup we see the head of the calf which Abraham used for the feast. The church interprets this calf as a prototype of the New Testament Lamb, and thus the cup acquires its Eucharistic meaning. The left and the middle angels bless the cup: The Father blesses His Son on his Deed, on His death on the cross for the sake of man's salvation, and the Son, blessing the cup, expresses his readiness to sacrifice Himself. The third angel does not bless the cup and does not participate in the conversation, but is present as a Comforter, the undying, a symbol of eternal youth and the upcoming Resurrection.