What does « Heart / To turn » mean in the Quran?

Say, "Whoever is an enemy to Gabriel - it is [none but] he who has brought the Qur'an down upon your heart, [O Muhammad], by permission of Allah, confirming that which was before it and as guidance and good tidings for the believers."

Those who do not know say, "Why does Allah not speak to us or there come to us a sign?" Thus spoke those before them like their words. Their hearts resemble each other. We have shown clearly the signs to a people who are certain [in faith].

And of the people is he whose speech pleases you in worldly life, and he calls Allah to witness as to what is in his heart, yet he is the fiercest of opponents.

Allah does not impose blame upon you for what is unintentional in your oaths, but He imposes blame upon you for what your hearts have earned. And Allah is Forgiving and Forbearing.

And [mention] when Abraham said, "My Lord, show me how You give life to the dead." [Allah] said, "Have you not believed?" He said, "Yes, but [I ask] only that my heart may be satisfied." [Allah] said, "Take four birds and commit them to yourself. Then [after slaughtering them] put on each hill a portion of them; then call them - they will come [flying] to you in haste. And know that Allah is Exalted in Might and Wise."

And if you are on a journey and cannot find a scribe, then a security deposit [should be] taken. And if one of you entrusts another, then let him who is entrusted discharge his trust [faithfully] and let him fear Allah, his Lord. And do not conceal testimony, for whoever conceals it - his heart is indeed sinful, and Allah is Knowing of what you do.

It is He who has sent down to you, [O Muhammad], the Book; in it are verses [that are] precise - they are the foundation of the Book - and others unspecific. As for those in whose hearts is deviation [from truth], they will follow that of it which is unspecific, seeking discord and seeking an interpretation [suitable to them]. And no one knows its [true] interpretation except Allah. But those firm in knowledge say, "We believe in it. All [of it] is from our Lord." And no one will be reminded except those of understanding.

[Who say], "Our Lord, let not our hearts deviate after You have guided us and grant us from Yourself mercy. Indeed, You are the Bestower.

And hold firmly to the rope of Allah all together and do not become divided. And remember the favor of Allah upon you - when you were enemies and He brought your hearts together and you became, by His favor, brothers. And you were on the edge of a pit of the Fire, and He saved you from it. Thus does Allah make clear to you His verses that you may be guided.

And Allah made it not except as [a sign of] good tidings for you and to reassure your hearts thereby. And victory is not except from Allah, the Exalted in Might, the Wise -

We will cast terror into the hearts of those who disbelieve for what they have associated with Allah of which He had not sent down [any] authority. And their refuge will be the Fire, and wretched is the residence of the wrongdoers.

Then after distress, He sent down upon you security [in the form of] drowsiness, overcoming a faction of you, while another faction worried about themselves, thinking of Allah other than the truth - the thought of ignorance, saying, "Is there anything for us [to have done] in this matter?" Say, "Indeed, the matter belongs completely to Allah." They conceal within themselves what they will not reveal to you. They say, "If there was anything we could have done in the matter, some of us would not have been killed right here." Say, "Even if you had been inside your houses, those decreed to be killed would have come out to their death beds." [It was] so that Allah might test what is in your breasts and purify what is in your hearts. And Allah is Knowing of that within the breasts.

O you who have believed, do not be like those who disbelieved and said about their brothers when they traveled through the land or went out to fight, "If they had been with us, they would not have died or have been killed," so Allah makes that [misconception] a regret within their hearts. And it is Allah who gives life and causes death, and Allah is Seeing of what you do.

So by mercy from Allah, [O Muhammad], you were lenient with them. And if you had been rude [in speech] and harsh in heart, they would have disbanded from about you. So pardon them and ask forgiveness for them and consult them in the matter. And when you have decided, then rely upon Allah. Indeed, Allah loves those who rely [upon Him].

And that He might make evident those who are hypocrites. For it was said to them, "Come, fight in the way of Allah or [at least] defend." They said, "If we had known [there would be] fighting, we would have followed you." They were nearer to disbelief that day than to faith, saying with their mouths what was not in their hearts. And Allah is most Knowing of what they conceal -

Those are the ones of whom Allah knows what is in their hearts, so turn away from them but admonish them and speak to them a far-reaching word.

And [We cursed them] for their breaking of the covenant and their disbelief in the signs of Allah and their killing of the prophets without right and their saying, "Our hearts are wrapped". Rather, Allah has sealed them because of their disbelief, so they believe not, except for a few.

So for their breaking of the covenant We cursed them and made their hearts hard. They distort words from their [proper] usages and have forgotten a portion of that of which they were reminded. And you will still observe deceit among them, except a few of them. But pardon them and overlook [their misdeeds]. Indeed, Allah loves the doers of good.

O Messenger, let them not grieve you who hasten into disbelief of those who say, "We believe" with their mouths, but their hearts believe not, and from among the Jews. [They are] avid listeners to falsehood, listening to another people who have not come to you. They distort words beyond their [proper] usages, saying "If you are given this, take it; but if you are not given it, then beware." But he for whom Allah intends fitnah - never will you possess [power to do] for him a thing against Allah. Those are the ones for whom Allah does not intend to purify their hearts. For them in this world is disgrace, and for them in the Hereafter is a great punishment.

So you see those in whose hearts is disease hastening into [association with] them, saying, "We are afraid a misfortune may strike us." But perhaps Allah will bring conquest or a decision from Him, and they will become, over what they have been concealing within themselves, regretful.

They said, "We wish to eat from it and let our hearts be reassured and know that you have been truthful to us and be among its witnesses."

And among them are those who listen to you, but We have placed over their hearts coverings, lest they understand it, and in their ears deafness. And if they should see every sign, they will not believe in it. Even when they come to you arguing with you, those who disbelieve say, "This is not but legends of the former peoples."

Then why, when Our punishment came to them, did they not humble themselves? But their hearts became hardened, and Satan made attractive to them that which they were doing.

Say, "Have you considered: if Allah should take away your hearing and your sight and set a seal upon your hearts, which deity other than Allah could bring them [back] to you?" Look how we diversify the verses; then they [still] turn away.

And We will turn away their hearts and their eyes just as they refused to believe in it the first time. And We will leave them in their transgression, wandering blindly.