In Torah, Aaron performed the miracle of the staff, "The LORD said to Moses and Aaron, "When Pharaoh says to you, "Perform a miracle," then say to Aaron, "Take your staff and throw it down before Pharaoh," and it will become a snake." So Moses and Aaron went to Pharaoh and did just as the LORD commanded. Aaron threw his staff down in front of Pharaoh and his officials, and it became a snake. Pharaoh then summoned wise men and sorcerers, and the Egyptian magicians also did the same things by their secret arts: Each one threw down his staff and it became a snake. But Aaron's staff swallowed up their staffs. Yet Pharaoh's heart became hard and he would not listen to them, just as the LORD had said." (Exodus 8-13)

But in Quran, Moses performed the miracle of the staff, "And when the magicians came, they said to Firon: Shall we get a reward if we are the vanquishers? He said: Yes, and surely you will then be of those who are made near. Musa said to them: Cast what you are going to cast. So they cast down their cords and their rods and said: By Firon's power, we shall most surely be victorious. Then Musa cast down his staff and lo! it swallowed up the lies they told. And the magicians were thrown down prostrate; They said: We believe in the Lord of the worlds: The Lord of Musa and Haroun." (The Poets. 41 – 48)

According to Biblical data, Aaron's rod blossomed and bore fruit in the Tabernacle, it was later stored in the Ark of the Covenant. Moreover, it was later used by David to slay Goliath. (1 Samuel 17:40) David handed the rod to his descendants, until its disappearance after the destruction of the First Temple.

The rod was made of sapphire and had a weight of 40 sheahs (1 sheah = 10.70 pounds), it bore the initials of the Ten Plagues. Haggadics tells us that that the rod was created on the sixth day of creation and was given to Adam when he was driven out of paradise. It was later passed to Shem, Enoch, Abraham, Isaac and Jacob, and then Joseph possessed it. When Joseph died Egyptian nobles stole the staff. Then, Jethro, father in law to Moses, possessed the staff.

Once Jethro planted the staff in his garden, no one could pull it out of the ground. Because the ineffable name of God was on the rod, no one dared to touch the rod, doing so was synonymous with death. When Moses entered Jethro's household, he read the name, and because of this, he was able to withdraw the rod. Zipporah, Jethro's daughter, was given to Moses in marriage because of this act.

Apart from the key miracle of the snake, the rod was also used to split the sea in order to escape Pharaoh. Another usage was when Moses people asked him for water in the wilderness, he struck rocks with his staff, and twelve springs gushed for the twelve tribes.

Reference:
http://jewishencyclopedia.com/view.jsp?artid=5&letter=A&search=Aaron's%20rod