Elder Oaks spoke on healing the sick, with section III being on priesthood blessings. He points out that "faith is essential for healing by the powers of heaven" and that "the greater responsibility is with him who is blessed." The person being blessed (be it any kind of priesthood blessings) plays a huge role in the part of a blessing, as does their faith. I have some of my strongest faith in blessings of healing. Twice in my life I have felt the healing power begin just from asking for a blessing.
Another part that is crucial to remember in a healing blessing is the will of the Lord. We don't pray to change Lord's will. We pray to align our will with the Lord. And if it be the Lord's will that a person not recover from an illness, or at least not recover for a time, then a blessing won't change that. Sometimes a blessing of healing is that the person who is ill (and those connected to them) will be able to accept the will of the Lord.
I'm not sure why my faith in blessings of healing is so strong. It just is. It always has been. And it has blessed me very much.