What does Matthew 10:41 mean?

Jesus is sending out the Twelve, His core group of hand-picked apostles (Matthew 10:1–4). Their current mission is to represent Him by teaching His message and performing His miracles in His name (Matthew 10:5–8). Christ has said that anyone who receives the apostles by believing in Jesus and offering hospitality also receives Jesus and the one who sent Jesus, God the Father (Matthew 10:40).

In addition, Jesus states that someone who receives a prophet because he is a prophet or a righteous person because he is a righteous person will receive a prophet or righteous person's reward. Put another way, someone who believes and helps a prophet or righteous person will have a share in the reward God will give to that prophet or righteous one.

This seems to put Christ's apostles on the same level as the prophets and righteous men of Israel's Old Testament history. A prophet was someone who was given a message by God to deliver to the people. Righteous people obeyed God by doing the specific work He assigned to them. The apostles, sent out by Jesus, both delivered God's message to the people and performed the righteous work of healing and casting out demons that He gave them to do.

The reward Jesus mentions includes eternal life in God's kingdom as well, perhaps, as special rewards that will be given to the apostles in that eternal home. The apostles will share those rewards with those who believed their message and offered hospitality to help them accomplish their work in Jesus' name.