Jesus went around to all the towns and villages, teaching in their synagogues, proclaiming the gospel of the kingdom, and curing every disease and illness. At the sight of the crowds, his heart was moved with pity for them because they were troubled and abandoned, like sheep without a shepherd. Then he said to his disciples, "The harvest is abundant but the laborers are few; so ask the master of the harvest to send out laborers for his harvest." Then he summoned his twelve disciples and gave them authority over unclean spirits to drive them out and to cure every disease and every illness. Jesus sent out these twelve after instructing them thus, "Do not go into pagan territory or enter a Samaritan town. Go rather to the lost sheep of the house of Israel. As you go, make this proclamation: 'The kingdom of heaven is at hand.' Cure the sick, raise the dead, cleanse lepers, drive out demons. Without cost you have received; without cost you are to give. (Mt 9:35-10:1,5-8)
Jesus went around the towns and villages proclaiming the kingdom. He was also curing the disease and illness. He was revealing and making present the kingdom in word and deeds. Why did he go around? Surely he was doing the same in the synagogues. Probably very few people were going to the synagogue or synagogue was open only for a limited time or it had its own timetable. Jesus did not want to be limited by time and space. He wanted the kingdom work to be done always and at anyplace and for everybody. Streets and roads were the only places which had not restriction of any sort. They (roads and streets and open spaces) were open at all times and for everyone.
Jesus did not want to hold on to the authority to himself: the authority to heal and to cast out demons and the authority to proclaim the gospel. Since the ministry was limitless (not limited by space and time and persons) and the demand was great (there were more people needing the assistance) he appointed twelve of his followers to continue or join in with him to do the same mission. Hence he shared his authority with them. The mission was important for him and all the other rules and restrictions were secondary. Probably this is what the mission priority means.
