"Provide neither gold nor silver nor copper in your money belts, nor bag for your journey, nor two tunics, nor sandals, nor staffs; for a worker is worthy of his food. Now whatever city or town you enter, inquire who in it is worthy, and stay there till you go out. And when you go into a household, greet it. If the household is worthy, let your peace come upon it. But if it is not worthy, let your peace return to you. And whoever will not receive you nor hear your words, when you depart from that house or city, shake off the dust from your feet. Assuredly, I say to you, it will be more tolerable for the land of Sodom and Gomorrah in the day of judgment than for that city."
Essentially, Jesus told His apostles not to pack any supplies for this evangelistic journey. They were to go as they were with the garment on their back, the sandals on their feet, and a staff to aid in walking and to protect them from common dangers (cf. Mark 6:8,9). They were not to take extras of anything, but rather they were to be provided for by the hospitality of the Jewish people for their bread and shelter.
The principle that "a worker is worthy of his food" is taught throughout the Scriptures (cf. I Cor. 9:14; I Tim. 5:18; Gal. 6:6). Their work would be to preach and perform miracles. This work would be performed swiftly and most effectively if the disciples weren't burdened with traveling supplies. It is unknown how long this evangelistic mission lasted, but anywhere from a couple of weeks to a few months is a reasonable guess. Regardless of the time frame, to travel in this manner with absolutely no food, supplies, or money would have taken great faith. It should be observed that Jesus' instructions here were of a temporary nature. Evangelists were not always prohibited from taking bread, money, and other basic supplies on their journeys (cf. Luke 22:35-38).
After giving His apostles power, limiting their territory, and telling them what to bring, He then proceeded to tell them how to conduct themselves on this evangelistic journey. They were not to change their lodging from house to house within a city because of pride or luxury (i.e., once they were provided with housing, they should stay with their "worthy" host until leaving that region).
The traditional form of greeting when entering a house was: "Peace to this house." The apostles were instructed to bless each home they entered, and they were assured that the peace prayed for would return to them if they were rejected. Those who would not welcome the apostles and their message were here labeled as not worthy. Jesus then began to warn them that their experiences would not always be pleasant. Sometimes they would have to leave a city and shake the dust off their feet (e.g., Acts 13:50,51; 18:6). The Jews considered the dust of the heathen countries to be polluted (cf. Amos 7:17), and they would shake it off of themselves when entering their own land. Thus, in this instance, this action would symbolize the unworthiness of any hard-hearted Jews who rejected the apostles. It would also signify that the apostles were free of any responsibility for these stubbornly rebellious souls (cf. Acts 20:26,27). To shake the dust off after leaving a house would indicate a partial rejection, but to shake the dust off after leaving a city would indicate a complete rejection in that area.
Jesus stated in Matthew 10:15 that it would be more tolerable for Sodom and Gomorrah in the final day of judgment than for a city that rejected the apostles and the gospel message (cf. 11:24). Since God judges all people in proportion to their opportunities (cf. Luke 12:47,48), any city that rejected the apostles and their message would be judged very harshly by God. It is not that this sin was of a more perverse nature than those of Sodom and Gomorrah. The problem was that they had been blessed with so many more opportunities to accept the truth and repent than Sodom and Gomorrah had, yet they continually refused.