Luke 24:13-35 says,
That same day two of them were going to a village called Emmaus, about seven miles from Jerusalem. They were talking with each other about everything that had happened. And as they talked and deliberated, Jesus Himself came up and walked along with them. But their eyes were kept from recognizing Him.
He asked them, “What are you discussing so intently as you walk along?”
They stood still, with sadness on their faces. One of them, named Cleopas, asked Him, “Are You the only visitor to Jerusalem who does not know the things that have happened there in recent days?”
“What things?” He asked.
“The events involving Jesus of Nazareth,” they answered. “This man was a prophet, powerful in speech and action before God and all the people. Our chief priests and rulers delivered Him up to the sentence of death, and they crucified Him. But we were hoping He was the One who would redeem Israel. And besides all this, it is the third day since these things took place.
Furthermore, some of our women astounded us. They were at the tomb early this morning, but they did not find His body. They came and told us they had seen a vision of angels, who said that Jesus was alive. Then some of our companions went to the tomb and found it just as the women had described. But Him they did not see.”
Then Jesus said to them, “O foolish ones, how slow are your hearts to believe all that the prophets have spoken! Was it not necessary for the Christ to suffer these things and then to enter His glory?” And beginning with Moses and all the Prophets, He explained to them what was written in all the Scriptures about Himself.
As they approached the village where they were headed, He seemed to be going farther. But they pleaded with Him, “Stay with us, for it is nearly evening and the day is almost over.”
So He went in to stay with them. While He was reclining at the table with them, He took bread, spoke a blessing and broke it, and gave it to them. Then their eyes were opened and they recognized Him; and He disappeared from their sight.
They asked each other, “Were not our hearts burning within us as He spoke with us on the road and opened the Scriptures to us?” And they got up that very hour and returned to Jerusalem.
There they found the Eleven and those with them, gathered together and saying, “The Lord has indeed risen and has appeared to Simon!”
Then the two told what had happened on the road, and how they had recognized Jesus in the breaking of the bread.
After his resurrection, and upon Jesus breaking bread in communion with two disciples, the disciples' eyes were opened, and they recognized Jesus.
Upon recognizing Him, Jesus disappeared from their sight.
What is the deeper meaning of this occurrence?