Why did God show Moses the signs of the rod and the leprous hand?
God gave Moses the signs of the rod becoming a serpent and the hand becoming leprous and then whole to convince Moses that he would be led by God and to prove that God meant what He said. These signs reassured Moses of divine backing for the mission to Pharaoh.
Les explains that God had already used the signs to convince Moses that he indeed was going to be led of God. The rod was thrown down and became a serpent; when picked up, it became a rod again. Then Moses placed his hand in his bosom, and it became leprous; when he took it out and put it back, it was whole. These signs, Les says, were to prove to Moses that God indeed meant what He said, addressing Moses' hesitation about approaching Pharaoh after forty years and his complaint that he was slow of speech and slow of tongue.