What does Luke 24:28 mean?

Cleopas and his friend have reached Emmaus. Over the course of their walk, they discussed what they've witnessed the last three days. They told Jesus' story to a fellow traveler whom they don't realize is Jesus and heard Jesus frame that story within Old Testament prophecy.

Now, they've reached the place where they're staying, perhaps an inn. The men invite Jesus to join them. He agrees, and when dinner is served, He takes the lead, taking the bread, blessing it, and passing out broken pieces (Luke 24:29–30).

It's at that point they realize who He is. It's impossible to say how many meals they've shared with Him—how many times they've seen His hands break bread and heard Him pray a blessing over it. As soon as they realize whom they've been walking with, Jesus disappears (Luke 24:31).

Jesus acts as if He's continuing His journey. We can't make too many moral judgments on cultures we don't understand. Within the culture, Jesus is not trying to deceive the men. He's not being passive-aggressive. He is acting according to the culture. It would be rude for Him to ask or assume He could eat with the men. To host someone is to take that person under your protection. When the men don't offer right away, Jesus gives them the opportunity to invite Him to stay. The Middle Eastern culture of hospitality demands that they do. Likely, their curiosity makes the decision an easy one.