What is the meaning behind the statement that hashem "hardened his heart"?

Since this is a classic question, I am sure that someone will right you a fully answer.

The classic question is how could HaShem hardened Pharoah's heart. Where was his free will?

1. HaShem made an exception in the case. It was part of Pharoah's punishment for mistreating the jews.
2. Pharoah had free will. HaShem just gave him the strength (fortified his heart) so he could continue making the wrong solution.
3. An extensive textual analysis which shows that Pharoah does exert free will and the phrase harden his heart refers to not listening to suffering of his people.

I don't know if this is relevant, but in ancient Hebrew, the heart is the seat of emotions and the kidney is the seat of the intellect. HaShem made his heart heavy. He didn't shut down his kidneys.

Aryeh Shore