The hand in the Bible represents power, which is easy to understand, so to reach out or stretch out the hand means to exercise power, to put it to work. This is an image that's used a great deal in the stories of Moses, who repeatedly stretched out his hand (or his rod, which represents a more external kind of power) to bring plagues on Egypt and perform other miracles. This is a correspondence that makes sense, since we reach out constantly to use our hands to do our work.