I bet you have always pictured Moses with a staff in his hand. No, it was the shepherd's rod that was in his hand. Moses was a shepherd and he undoubtedly had both a staff and a rod. It was the rod that was lifted up over the river. It was the rod that was taken into the presence of Pharaoh. It was the rod that turned into a snake. It was that snake that ate up Pharaoh's magicians' snakes, and Moses had to pick it up, whereupon it turned back into a rod. Since it was the rod, He said:
The word that is translated rod is not the same one that is translated rod in Psalm 23, but the implication and usage are the same.
What did Moses do with the rod? It was by the rod that God, through Moses, demonstrated His authority and power. The rod became a serpent. The rod was waved over the river, and the water turned into blood. It was the rod by which God demonstrated His authority and power that was invested in Moses. The rod was an extension, symbolically, of God's will, of His power, of His strength, of His mind, of His wisdom.