The Surah derives its name from the initial letter Qaf, thereby implying that it is the Surah which opens with the alphabetic letter Qaf.
There is no authentic tradition to show as to when exactly this Surah was sent down. A study of the subject matter, however, reveals that its period of revelation is the second stage of the Holy Prophet's life at Makkah, which lasted from the third year of the Prophethood till the fifth year. We have given the characteristics of this period in the Introduction to the Surah Al-An'am. In view of those characteristics it can be said that this Surah might have been sent down in about the 5th year, when the antagonism of the disbelievers had become quite intense but had not yet assumed tyrannical proportions.
Authentic traditions show that the Holy Prophet used to recite this Surah generally in the Prayer on the Eid days. A woman named Umm Hisham bin Harithah, who was a neighbor of the Holy Prophet, says that she was able to commit Surah Qaf to memory only because she often heard it from the Holy Prophet in the Friday sermons. According to some other traditions he often recited it in the Fajr Prayer. This makes it abundantly clear that this was an important Surah in the sight of the Holy Prophet. That is why he made sure that its contents reached as many people as possible over and over again.
This reason for this importance can be easily understood by a careful study of the Surah. The theme of the entire Surah is the Hereafter. When the Holy Prophet started preaching his message in Makkah what surprised the people most was the news that people would be resurrected after death, and they would have to render an account of their deeds. They said that that was impossible; human mind could not believe that that would happen. After all, how could it be possible that when the body had disintegrated into dust the scattered particles would be reassembled after hundreds of thousands of years to make up the same body once again and raised up as a living body, Allah in response sent down this discourse. In it, on the one hand, arguments have been given for the possibility and occurrence of the Hereafter in a brief way, in short sentences, and, on the other, the people have been warned, as if to say: "Whether you express wonder and surprise, or you regard it as something remote from reason, or deny it altogether, in any case it cannot change the truth. The absolute, un-alterable truth is that Allah knows the whereabouts of each and every particle of your body that has scattered away in the earth, and knows where and in what state it is. Allah's one signal is enough to make all the scattered particles gather together again and to make you rise up once again as you had been made in the first instance. Likewise, your this idea that you have been created and left free to yourselves in the world and that you have not been made answerable to anyone, is no more than a misunderstanding. The fact is that not only is Allah Himself directly aware of each act and word of yours, even of the ideas that pass in your mind, but His angels also are attached to each one of you, who are preserving the record of whatever you do and utter. When the time comes, you will come out of your graves at one call just as young shoots of vegetable sprout up from the earth on the first shower of the rain. Then this heedlessness which obstructs your vision will be removed and you will see with your own eyes all that you are denying today. At that time you will realize that you had not been created to be irresponsible in this world but accountable to all your deeds the meeting out of the rewards and punishments, the Hell and Heaven, which you regard as impossible and imaginary things, will at that time become visible realities for you in consequence of your enmity and opposition to the Truth you will be cast into the same Hell which you regard as remote from reason today and the ones who fear the Merciful God and return to the path of righteousness, will be admitted to the same Paradise at whose mention you now express wonder and surprise.
Source: Sayyid Abul Ala Maududi - Tafhim al-Qur'an - The Meaning of the Quran