Recently someone asked a great question about God hardening people’s hearts in Scripture.
Fourteen times in Scripture a statement is made that God hardens someone’s heart (15 if we count John 12:40 where the “He” may be read as a reference to God or perhaps to Isaiah –see Isaiah 6:9-10). Nine of those times are in relation to Pharaoh. 
In most of the cases throughout Scripture, it’s clear that God hardens hearts only after a long track record of disobedience. But when someone, such as Pharaoh, maintains their willful disobedience, then decides to let up on it in order to ease the painful consequences (e.g. to escape a plague), God may say, “No, you are not truly repenting, therefore I will harden your heart to keep you from stopping your sinful actions only to make things easier on yourself. I will not let you use me. But after giving you a lifetime of freedom to choose, I will now use you to accomplish my purposes, because I am God and you are not.”
The hardening of the heart is essentially a sort of final judgment of God that takes place before someone dies. It’s as if God considers now fixed someone’s evil heart as it has become over a lifetime. He cements the deal, so to speak, solidifying the history of their own willful sinful choices, which He now considers their definitive condition, and then forces them to act accordingly and face the consequences they would otherwise have tried to avoid. (For more on God’s sovereignty trumping people’s plans, check out Psalm 115:3, Proverbs 16:9, Genesis 50:20, Isaiah 40:23, and 2 Chronicles 20:6.)
That’s my take on it, and here are the links that all have something unique to contribute on the meaning of God hardening hearts: