WE GRANTED THEE AN ABUNDANCE OF BLESSING!
VERSES NO. 1-3
This sura (like the suras of Morning Light and The Expansion is completely addressing Prophet (SA). One of the important objectives of these three suras is to comfort him against so many of painful events and adversaries' repeated diatribes.
What is meant by Abundance (Kowsar) here? There is a tradition stating that when the sura was revealed, Prophet (SA) sat on the pulpit and recited the sura. The companions asked: What God has granted to thee?
He said: It is a river in the paradise, whiter than milk, smoother than crystal, in both parts of which there are canopies made of pearl and ruby.
It has been interpreted to prophethood, Quran, multitude of companions, multitude of children and offspring (all of whom are from the generation of his daughter, Fatima (AS)).
Some too have interpreted it to intercession.
However, apparently Abundance has a wide scope of meaning, and what was mentioned above are some of its clear implications. There are many other connotations which could be mentioned for interpretation of the verse.
We shall remember that when God gave the tidings to His prophet, the result of the abundance of blessing had not appeared yet. It was a tiding about the near and far future; a miraculous tidings indicating the truthfulness of Prophet's (SA) invitation. 
However, this great blessing calls for a great gratitude, although the created could never fulfill perfectly what the creator deserves, but the success for paying gratitude is a blessing by itself! 
That is right! He is the giver of blessing. Therefore, prayer, worship and sacrifice for else than Him is nonsense. 
This is against the idolaters who prostrated before and sacrificed for the idols, while believed that their blessings belong to God! 
Application of the term without posterity implies that their enmity was so mingled with cruelty and roguery that they even did not observe least courtesy in their enmity. 

Hazrat Fatima (AS) and Abudance!
We said that Abundance has a wide and comprehensive scope of meaning, that is, abundance of blessing and goodness. However, many of great Shiite Ulama believe that one of its clearest implications is the blessed existence of Fatima Zahra (AS), because according to the occasion of revelation, they accused Prophet (SA) to being without posterity. Quran negates them and says: We granted thee the Abundance.
This interpretation implies that the abundance of blessing is the same Fatima (AS) because the generation and posterity of Prophet (SA) was spread in the world through his esteemed daughter. Not only his generation belonged to the Prophet (SA) corporeally, but also they preserved and protected his religion and all Islamic merits and declared them to the next generations. They are Imams from the Prophet's Household (AS) who are very honorable.
We find an interesting discussion by Fakhr Razi in this regard who says: The third idea is that the sura is revealed for refuting those who criticized Prophet (SA) for not having a child. Therefore, the sura means that God grants him a generation which survives by lapse of time. You can see how many of Prophet's Household were martyred, but the world is full of their generation. On the other hand, no remarkable person exists in the world from Umayyad (who were Islam adversaries). Again, you can find many of great Ulama among them, such as, Imam Bagher, Imam Sadiq and Imam Reza (AS).
Thousands of thousand of Fatima's (AS) offspring are now spread throughout the world, among whom we can find great writers, Faqih, interpreters, traditionists and commanders.

THE END OF ABUNDANSE SUREH