This is…an outstanding praise of hospitality, in order that we may be sure that God Himself is in our home, is being fed at our house, is lying down and resting as often as some pious brother in exile because of the Gospel comes to us and is received hospitably by us. This is called brotherly love or Christian charity; it is greater than that general kindness which is extended even to strangers and enemies when they are in need of our aid.
For the accounts of the friendships of the Gentiles, like those of Theseus and Hercules, of Pylades and Orestes, are nothing in comparison with the brotherhood in the church; its bond is an association with God so close that the Son of God says that whatever is done to the least of His is done to Himself. Therefore their hearts go out without hypocrisy to the needs of their neighbor, and nothing is either so costly or so difficult that a Christian does not undertake it for the sake of the brethren.
But if anyone earnestly believed that he is receiving the Lord Himself when he receives a poor brother, there would be no need for such anxious, zealous, and solicitous exhortations to do works of love. Our coffers, storeroom, and compassion would be open at once for the benefit of the brethren. There would be no ill will, and together with godly Abraham we would run to meet the wretched people, invite them into our homes, and seize upon this honor and distinction ahead of others and say: “O Lord Jesus, come to me; enjoy my bread, wine, silver, and gold. How well it has been invested by me when I invest it in You!”
Martin Luther, Commentary on Genesis 18:5, LW 3:189-190