To clarify the meaning of verses 61 to 62 of Surah al-Waqe'ah, we have to study verse 60 of the same chapter as well; because these three verses are closely connected, in fact, they express the reason and wisdom behind ordaining death and resurrection of  humans in the Hereafter. Therefore we must review these three verses in an orderly manner.
1. In Surah al-Waqe'ah verse 60, God says: "We have ordained death among you and We are not to be overcome"[1] To handle the affairs of creatures with all their characteristics is a necessary component of creation and life-giving. When God grants existence to man, He grants him limited existence. From the very beginning of his conception to the end of his life in this world as well as every characteristic that he acquires and abandons are all components and necessary parts of that limitation ordained and measured by God. One of these characteristics is death. Thus man's death like his life is ordained by God, not that God has been unable to create man for eternity; and not that He has not been able to create such a creation and His power is limited to create a creature that lives for example 70 years and necessarily dies after that period. It is also not true to say that God has created man to live forever in this world but destructive factors overcome God's will and kill the creature; because these two premises necessitate God's power to be limited. In first premise He has not been able to grant more endurance to His living creature, and in second premise He has not been able to prevent the attack of destructive forces, and these premises do not extend to God; because His power is absolute and He is undefeatable.
From what has been said earlier it becomes clear that "We have ordained death among you" means to make one understand that first, death is a truth and second it is ordained by God, not that it is a necessary part of a living creature, rather it has been ordained for that creature by God; He has created the creature to live for a specific period of time and die at a specific time and depart to another world.
Therefore, with this introduction it becomes clear that "We are not to be overcome" means –taking into account that sabq means to overcome and masbooq means to be overcome- that God is not overcome and defeated by destructive forces when death happens to a living creature and it is not that He grants people eternal life but those forces overcome His will and cancel the life that He wants to be eternal.
2. The Quran says:

«عَلى‏ أَنْ نُبَدِّلَ أَمْثالَکُمْ وَ نُنْشِئَکُمْ فی‏ ما لا تَعْلَمُون»

“In order that We may bring to your place the likes of you and make you grow into what you know not”
According to previous verse, this verse means that We have ordained death among you while it has been ordained to make room for the likes of you and to replace you by others, and We resurrect you in another life of which you are not aware. The term "amthal" is the plural form of the Arabic term "methl" [2]and "methl" of something is something that falls in the same category of being. More clearly, it is another instance for the same category, for example Tom which is similar to John; that is another example of the category of man. And "In order that We may bring in your place the likes of you" means that We will replace you with the likes of you.
Anyway, it means that He will replace a group of humans with another group of humans and a generation with another generation and older generation is replaced by younger generation. The Arabic word "ma" in the original verse is a conjunction and refers to creation and the sentence has been added to the sentence starting with “We may bring…” and it is implied to be like this "We are not to be overcome. In order that We may bring in your place the likes of you and We are not to be overcome and make you grow into what you know not". It means We have ordained death to replace your generation with another generation and grant you another creation of which you are not aware and that is: being in the Hereafter which is not like the unsustainable nature of the being in this world.
In short, the meaning of these two verses is: We have ordained death among you, not because of a lack in our power and not that we are unable to provide necessities for your life to continue, rather We have created you on this basis that you die after an appointed time; since Our creation is based on changing the likes; a group dies and makes room for another group, and make people of the past die and replace them with a new generation.  It is also on this basis that We grant you another creation unlike the transitory creation of this world, therefore death is: movement from a house to another house and from a creation to a better creation and does not equal annihilation.
3. The Quran says:

«وَ لَقَدْ عَلِمْتُمُ النَّشْأَةَ الْأُولى‏ فَلَوْ لا تَذَکَّرُون»

“And certainly you know the first growth, why do you not then mind?”
This verse expresses a logical deduction to prove afterlife through our knowledge of life in this world and its characteristics.
"The first growth" means this world and "know" means knowledge of its characteristics which requires the belief in another world which is eternal. A world where our deeds are rewarded, because it can be certainly inferred from the amazing system of this world that there is nothing meaningless in this world and there is certainly an eternal and everlasting purpose for life in this world. Another necessity of this world's system is that every creature has been guided toward the goal it has been created for. Man should be guided via sending prophets, lawmaking and amr bil ma'roof [enjoining the right] and nahy anil monkar [forbidding from evil] toward guaranteeing his happiness. This also necessitates that rewards be assigned to good deeds and punishment for bad deeds. Since this world is very limited for reward and punishment there is no choice but to have another world to completely fulfill reward/punishment.
But how is it possible to resurrect humans? It is well reasoned in life of this world because they saw and understood in this world that the same God who has created this world out of nothing can create it for a second time as well:"Say: He will give life to them Who brought them into existence at first"[3] This itself is an argument for the possibility of resurrection and an answer to those who doubt it.
In short, with knowledge of this world, man can achieve the knowledge needed for groundwork of this argument, an argument that demonstrates the possibility of resurrection and gives an answer to those who doubt it. In other word once the possibility of resurrection is demonstrated, it is meaningless to doubt it. This argument –as you read above- is an argument for the possibility to resurrect dead bodies. It yields that the body which will be resurrected on the Day of Resurrection and will be rewarded or punished, is the same as the body in this world and when it is possible to create a body in this world and give it life then it is possible to create a body in the Hereafter and give it life, because they are similar to each other, and similar things have similar rulings in terms of possibility and impossibility.[4]
The most clear and informative interpretation for this verse is a saying from the Commander of the Faithful, Imam Ali (A) who says:

«...وَ عَجِبْتُ لِمَنْ أَنْکَرَ النَّشْأَةَ الْأُخْرَى وَ هُوَ یَرَى النَّشْأَةَ الْأُولَى ...»

"I am surprised at one who doubts the Hereafter and resurrection while he observes [the life of] this world". [5]
To sum up, this verse draws man's attention to the fact that when you witnessed your worldly mode of existence and covered the various stages of your life from the time of conception, when you were but an embryo, until you completed the living circle, then how can you deny the afterworld and the Day of Resurrection?!

---