What does Luke 24:37 mean?

Very recently, some of the men in this room had joined the women standing at a distance, watching Jesus hang on a cross (Luke 23:49). They saw the nails through His wrists and feet. They watched the blood run down from His body from the wounds He'd received by the soldiers and the temple guards. They watched Him struggle to breathe. They watched Him die. And some of them saw the soldier thrust a spear into His side, water and blood pouring out of the wound when the spear drew out (John 19:34–35).

About twelve hours ago, these same men listened as the women told them Jesus' grave was empty. An angel told them He had risen from the dead. Then, they saw Him! Peter and John returned to verify the tomb was empty. Then Peter saw Him. Then two men who had met Him on their way to Emmaus returned and told their story (Luke 24:1–35).

It's very possible some of these men had seen Jesus raise Lazarus from the dead, but that was different. Lazarus's body hadn't been beaten, whipped, nailed, and pierced. And Jesus had been there to call him from his tomb (John 11). There was no one to raise Jesus.

So, when Jesus appears in a glorified body, cleaned of blood, His expression cleared of pain and anguish, the only thing they can think is that they're seeing His spirit—not unlike when He walked on water (Mark 6:45–52). This time, His appearance is even more startling. How could a body recover from such wounds? How could Jesus be alive again?

Jesus understands and shows great patience. He points out His hands and feet. He eats fish—which no spirit could do (Luke 24:38–43). The disciples' reaction improves—slightly: fear and disbelief turn to joy and disbelief (Luke 24:41).