Exodus 7:12b

"But Aaron's staff swallowed up their staffs." NIV translation

When Aaron's staff swallowed the others, it was a statement concerning the supremacy of God. 

Satan and his demons, as represented by the other snakes, were eliminated by God.

Exodus 7:13

"Yet Pharaoh's heart became hard and he would not listen to them, just as the Lord had said." NIV translation

This was a warning shot in this "battle of the gods" but Pharaoh was full of pride and would not accept the word. This is the operating pattern of God and his judgment. He always gives a warning and, after it is ignored, He will bring the judgment.

Exodus 7:14 & 15

"Then the Lord said to Moses, 'Pharaoh's heart is unyielding; he refuses to let the people go. Go to Pharaoh in the morning as he goes out to the river. Confront him on the bank of the Nile, and take in your hand the staff that was changed into a snake.'" NIV translation

The Nile was like the giver of life to the people of Egypt and, because of Pharaoh's arrogant refusal, God told Moses to confront him there. He was also told to take the staff that had been changed into a snake as a reminder to Pharaoh. The pattern for this coming judgment is that God will send Moses and Aaron with a another warning followed by a series of three plagues. This pattern will occur three times and we are reminded that, throughout the Bible, three is associated with the earthly display of God's will for man.