The Veil over the Hearts of the Idolators
Allah says to His Messenger Muhammad;
وَإِذَا قَرَأْتَ الْقُرانَ جَعَلْنَا بَيْنَكَ وَبَيْنَ الَّذِينَ لَا يُوْمِنُونَ بِالاخِرَةِ حِجَابًا مَّسْتُورًا
And when you recite the Qur'an, We put between you and those who believe not in the Hereafter, an invisible veil.
Qatadah and Ibn Zayd said,
"It is coverings over their hearts,"
as Allah says;
وَقَالُوا قُلُوبُنَا فِي أَكِنَّةٍ مِّمَّا تَدْعُونَا إِلَيْهِ
وَفِي اذَانِنَا وَقْرٌ وَمِن بَيْنِنَا وَبَيْنِكَ حِجَابٌ
And they say;"Our hearts are under coverings (screened) from that to which you invite us; and in our ears is deafness, and between us and you is a screen. (41;5)
meaning, there is something that is stopping and preventing your words from reaching us.
حِجَابًا مَّسْتُورًا
an invisible veil.
meaning something which covers, or that cannot be seen, so there is a barrier between them and guidance.
This is the interpretation that Ibn Jarir (may Allah have mercy on him) thought was correct.
Al-Hafiz Abu Ya`la Al-Mawusili recorded that Asma' bint Abi Bakr (may Allah be pleased with her) said,
"When the Ayah,
تَبَّتْ يَدَا أَبِي لَهَبٍ وَتَبَّ
(Perish the two hands of Abu Lahab and perish he!), (111;1) was revealed, the one-eyed woman Umm Jamil (the wife of Abu Lahab) came with a stone pestle in her hand, screaming, `What was sent to us is somebody blameworthy, or, we reject somebody blameworthy
(Abu Musa - one of the narrators - said, it is I who am not sure what was said);
we shun his religion and disobey whatever he commands!'
The Messenger of Allah was sitting with Abu Bakr by his side. Abu Bakr, may Allah be pleased with him, said, `This woman has come and I am afraid she will see you.'
The Prophet said,
إِنَّهَا لَنْ تَرَانِي
(Certainly she will not see me), and he recited Qur'an through which he was protected from her;
وَإِذَا قَرَأْتَ الْقُرانَ جَعَلْنَا بَيْنَكَ وَبَيْنَ الَّذِينَ لَا يُوْمِنُونَ بِالاخِرَةِ حِجَابًا مَّسْتُورًا
And when you recite the Qur'an, We put between you and those who believe not in the Hereafter, an invisible veil.
She came and found Abu Bakr, but she did not see the Prophet.
She said, `O Abu Bakr, I have heard that your companion is lampooning me.'
Abu Bakr said, `No, by the Lord of this House (the Ka`bah), he is not lampooning you.'
Then she went away, saying, `The Quraysh know that I am the daughter of their master."