But their eyes were kept from recognizing him.
(Luke 24:16, ESV)
This verse has a previous question, but is important to the meaning of when their eyes were open: In Luke 24:16 why were the disciples eyes kept from recognizing Jesus, then opened?
They need the eyes of their heart opened before they could see.
Jesus said, “For judgment I came into this world, that those who do not see may see, and those who see may become blind.”
(John 9:39, ESV)
First Jesus opened the door to their hearts.
And he said to them, “O foolish ones, and slow of heart to believe all that the prophets have spoken! 26 Was it not necessary that the Christ should suffer these things and enter into his glory?” 27 And beginning with Moses and all the Prophets, he interpreted to them in all the Scriptures the things concerning himself.
(Luke 24:25–27, ESV)
They later acknowledged:
They said to each other, “Did not our hearts burn within us while he talked to us on the road, while he opened to us the Scriptures?”
(Luke 24:32, ESV)
They needed their hearts open to see with their eyes.
When he was at table with them, he took the bread and blessed and broke it and gave it to them. 31 And their eyes were opened, and they recognized him. And he vanished from their sight.
(Luke 24:30–31, ESV)
When Jesus broke the bread, it was probably the first time they saw his hands. The only physical description we have of Jesus is the scars on his hands, feet, and side. They needed to believe Jesus had risen before the recognized him. There unbelief and lack of hope played a part in their eyes of their heart initially being shut.
P.S.
Here's what happened with some when Jesus appeared before the great commission without opening their hearts.
Now the eleven disciples went to Galilee, to the mountain to which Jesus had directed them. 17 And when they saw him they worshiped him, but some doubted.
(Matt. 28:16–17, ESV)