Street Preacher Jesse Morell explains the Biblical meaning of “Hardening Hearts”:

Here is a modern analogy: When I preach on campus and sinners reject the message, people often tell me, “You are turning people off.” Now, I am not directly going into their hearts and turning them off to the truth. I do not have direct control over their choices. They are free moral agents. But the result of me preaching the uncompromising truth is that many sinners turn themselves off to it…

Notice that in the original passage, it was the job of the preacher to blind their eyes. It was not something God was directly going to do, but something that He did through the preacher. The original scripture is, “Make the heart of this people fat, and make their ears heavy, and shut their eyes; lest they see with their eyes, and hear with their ears, and understand with their heart, and convert, and be healed.” Isa 6:10…

This understanding of the modus operandi by which God hardens the hearts of sinners helps us to understand the other passages that speak of God hardening Pharaoh’s heart, which Calvinists also use as proof-texts for their doctrine that God doesn’t want everyone to repent and be saved. The Scriptures declare that God hardened Pharaoh’s heart (Exo. 7:13, 10:1; 10:20; 10:27; 11:10), but the Bible also says that Pharaoh hardened his own heart (Exo. 8:15; 32; 9:34). It was by sending Moses with his message and by performing miracles that God hardened Pharaoh’s heart.