I thought that only those with the priesthood can perform miracles like healing. But in class, we read a story of a young boy who blessed his father without the Melchizedek Priesthood. Futhermore, missionaries told of their experiences of people being healed from people of other faiths. How is this possible?
A very similar event happened during the ministry of Jesus Christ. Mark 9:38-40
38 And John answered him, saying, Master, we saw one casting out devils in thy name, and he followeth not us: and we forbad him, because he followeth not us.
39 But Jesus said, Forbid him not: for there is no man which shall do a miracle in my name, that can lightly speak evil of me.
40 For he that is not against us is on our part.
While the gift of healing is a part of priesthood authority, it is not exclusive to priesthood authority. The gift of healing is a very real spiritual gift that operates independently of the priesthood now and again. Even at that, it operates based upon faith. The full power of faith is something I feel we barely understand in this life, and these non-priesthood healing events are indicators of what may well be the love of God operating in the lives of his faithful children.