What does Matthew 10:11 mean?

This continues Jesus' instructions to His twelve hand-picked disciples. Matthew has renamed them apostles, using a Greek term that refers to someone "sent out" with the message of their master. These men are transitioning from students to "sent ones."

The Twelve will head out into the region of Galilee in pairs, travelling from town to town and preaching in the name of Jesus that the kingdom of heaven in near (Matthew 10:1–4). They will demonstrate that their message is true by displaying the power of Jesus to heal diseases and cast out demons (Matthew 10:5–8).

Jesus has told them not to take any extra provisions with them. God will provide all they need through the people they minister to in each town. They must not charge for their services of healing and preaching, but they should expect those who are helped to offer them hospitality and provision.

Now Jesus gets more specific. When they come into a new town or village, the disciples should find out who is "worthy" and stay with them until they leave town. In this case, worthy does not describe those who are most religious or the least sinful. By worthy, it will become clear, Jesus means those who are ready to repent and believe the message of Christ's apostles.

Jesus implies that some among that group will gladly welcome a pair of Jesus' representatives to stay with them while they're in the area. In receiving them, they will be receiving Jesus Himself.