Aaron was the brother of Moses in the Old Testament. Aaron's rod refers to any of the staves he carried, and the miraculous powers they displayed. Aaron turned his rod into a serpent which then ate the serpent-rods of Pharoah's sorcerers.
This passage refers to another miracle, when Moses used a rod to part the Red Sea. He may or may not have borrowed it from his brother, but this instrument of deliverance is usually called "Moses's rod".
And the LORD said unto Moses, Wherefore criest thou unto me? speak unto the children of Israel, that they go forward:
But lift thou up thy rod, and stretch out thine hand over the sea, and divide it: and the children of Israel shall go on dry ground through the midst of the sea.
Exodus 14: 15-16