What does Matthew 14:16 mean?

The disciples literally lived to serve Jesus. Their primary work was to learn from Him, but a disciple of any master also agreed to serve him in exchange for their training. Jesus' disciples, especially, had begun to understand they would spend their entire lives serving Jesus by ministering to others.

Expected or not, this would have been difficult at times. In this case, the men planned to arrive at a desolate place to be alone, not to spend the day serving Jesus as He healed crowds of sick people. Now it was time for the evening meal and neither they nor the crowds had food to eat. Very reasonably, if not very compassionately, they suggested to Jesus that He send the people to nearby villages to get themselves food.

Jesus rejects that plan. The people don't need to leave. The disciples should give them food, Jesus says. The disciples knew for a fact that this was impossible. They simply did not have the resources to do what Jesus asked. Other gospels include their understanding that this would have required far more bread, and far more money, than were available (Mark 6:37; John 6:6–7). He would show them that His power makes anything possible.