What happens to the heart when a person sins?

A black spot appears on it. If he desists and repents, the heart becomes clear again. If he persists, the marks accumulate until they overshadow the heart, and that is the rust the Qur'an speaks of.

The Messenger of Allah ﷺ said: “Whenever a servant commits an act of wrongdoing, a black spot appears on his heart and when he desists, and seeks forgiveness, and repents, his heart will become clear. But, if he again commits the same wrongs, more and more black marks will accumulate until they overshadow his heart. This is the rust which the Almighty speaks of in the Qur'an” [Qur'an, al-Mutaffifin 83:14; Jami at-Tirmidhi 3334]

Imam Ghazali rahimahullah said, “Ignorance of Allah is a deadly poison and disobedience its disease. Knowledge of Allah is its antidote and obedience its medicine; there is no other way to heal the heart without medicine.” [al-Ghazali, Deliverance from Error, Al-Munqidh Min Al-Dalal 58]

Imam Ghazali rahimahullah, at the pinnacle of his career, left for ten years and spent that time with the great Sufis of his age. Only with that illumination did he write his masterpiece, Ihya' 'ulum al-din, and described the heart as the locus of the knowledge of Allah.