OCCASION OF REVELATION
It has been narrated from Ebne Abbas that when the verse,
و انذر عشیرتک القربین
(Poets, 26:214), was revealed, and the prophet was commissioned to warn his near relatives and invite them to Islam (or announce his invitation), Prophet (SA) came to Safa mountain and called: یا صباحاه! (This phrase was normally applied by Arab when they were assaulted by enemy and in order to warn all for encounter). When the people of Mecca heard his voice, they asked: Who is calling?
It was said: He is Mohammad. The people went to him.
He asked: Let me know do you believe me if I inform you that the enemy's riders are coming to assault you?
They replied: We have never heard a lie from you.
He said: انی نذیر للکم بین یدی عذاب شدید, that is, I warn you against a severe divine chastisement (I invite you to monotheism and abandonment of idols). When Abou Lahab heard it, he said: May you suffer loss and death! Have you gathered us just for this phrase?
Then the sura was revealed.
Some have added that when Abou Lahab's wife (Omme Jamil) was informed that the sura has been revealed about her and her husband, she came to Prophet (SA) having a stone at her hand while not seeing the Prophet. She said: I have heard that Mohammad has satirized me. By God, I will throw this stone to his mouth if I find him! I am too a poet! Then, she stated poems blaming Prophet and Islam. 
The danger of Abu Lahab and his wife for Islam and their enmity was not limited to this. There are much more reasons for addressing them and rebuking them explicitly in Quran to which will be referred later.

MAY THE HANDS OF ABU LAHAB BE CUT!
VERSES NO. 1-5
As we referred above in occasion of revelation of sura, the sura is in fact a reply to the vulgar utterances by Abu Lahab, Prophet's (SA) uncle and son of Abdol Motallab who was one of the obstinate adversaries of Islam.
In has been narrated that someone called Tariq Mehrabi says: I was in Zelmajaz market (Zelmajaz is located in Arafat near to Mecca). Once, I saw a young man crying: O people! Say there is no God save Allah (ال اله اال اهلل) to prosper. I saw another man following him throwing stones towards him so that his feet were bleeding. He was crying: O People! He is a liar. Do not believe in him!
I asked: Who is this young man?
It was said: He is Mohammad. He supposes to be a prophet and the other man is his uncle, Abu Lahab who is calling him a liar. 
We read in another narration: When a group of Arabs entered Mecca from outside, they referred to Abu Lahab for his relation with Prophet (SA) and his old age, and asked him about Prophet (SA). He said: He is a magician and they returned without seeing Prophet (SA). Later, a group came who said we do not return unless after seeing him. Abu Lahab said: We are trying cure his madness! Death be upon him!
It is well understood from above narrations that in many cases he pursued Prophet (SA) and did not spare any sabotage. He had a very obscene and tainted tongue and applied vulgar phrases. This is the reason why the above verses criticize him and his wife, Omme Jamil, so explicitly and violently. 
He was a rich man and relied on his wealth for his anti-Islamic attempts.
If his name is Abu Lahab, and the fire for his punishment too is a flaming (ابولهب) and great fire.
Not only for Abu Lahab, but also for none of the unbelievers and evil doers, their properties, wealth and social position relieve them from the fire of hell and divine chastisement. 
It has been narrated that after the battle of Badr and the defeat of Qureysh idolaters, Abu Lahab who had not participated personally in the battlefield asked Abousofyan when he returned about the event.
Abousofyan described for him how Qureysh host was defeated and then added: By God, we saw horsemen between the sky and earth supporting Mohammad! 
Here, Abu Rafe', one of slaves of Abbas says: I was sitting there. I raised my hand and said: They were heavenly angels. Abu Lahab became furious and beated me.
Then, Abbas's wife, Omme Afzal took a piece of wood and stroke it to Abu Lahab's head and said: Have you found this weak man alone!
Abu Lahab's head was broken and bled. After seven days, his body became infectious and he died for the disease. 
His body's infection was so much that none dared to approach him. He was moved to outside of Mecca and buried there.
There is no doubt that his wife has been Abousofyan's sister and Moavieh's aunt, who participated in her husband's enmities and sabotages. Then why is she called a lady who will carry upon her neck a halter of palm-fiber? Some believe that the reason is that she carried barbed brushed on her shoulder and pour it along the way of Prophet (SA) to hurt his feet.

THE END OF THE PALM FIBER SUREH