There are two reasons why this was an incredible action on Jesus’ part.
First, there was the physical aspect of Jesus’ action. Leprosy was, in the ancient world, incurable. It was also believed to be highly contagious. This was one reason why lepers were excluded from contact with other people; there was a desire to keep them from spreading their disease. To touch a leper in those days would have been similar to doing something like touching a person with AIDS if they were bleeding and you had a cut on your hand. It would be practically asking to be infected with a fatal and incurable disease. Jesus’ disciples would have been horrified and terrified by this action.
Second, there was also a spiritual aspect to this. Lepers were, by Jewish law, completely cut off from religious ceremonies. They were essentially excluded from the presence of God (remember, this was a faith for whom ritual observances were very important) because they could not go in temples. A person who had leprosy was ritually unclean on a permanent basis and could therefore never participate in religious observances. Therefore, by touching the leper, Jesus was risking (at least in the eyes of his disciples) the possibility of being cut off from God forever.
Thus, this was an act of incredible bravery both on a physical and on a spiritual level.