Q. If after the end of Kali-yuga , Satya-yuga is to come, then what is the purpose of the formation, maintenance and destruction of the universe over and over again?

A. The entire purpose of this process of creation, maintenance and destruction is to give the living entities a chance to return back home, back to the Spiritual world which is our eternal home. But when a  jiva wants to enjoy separately from God (Krishna), he is sent to this material world which is created just to facilitate his illusory enjoying mentality. We are eternally servants of Krishna but when we develop the mood of being a master or an enjoyer we fall down. Just like our hand, as long as it is connected to the body, it is useful. But when it is separated from the body, it becomes useless. Similarly as long as we are connected to God,we are valuable but when we separate ourselves,we become worthless. 

But the Supreme Lord is very merciful. He wants all of His parts and parcels to come back to Him. So He creates this material world and this cycle of yugas and also gives the process in every yuga by which we can go back to Him. So the first Yuga is Satya-yuga which is a very pious age and people are devotees and most of them make full use of the conducive opportunity to return to the kingdom of God. Those who do not take advantage of this opportunity come to Treta-yuga where the religiosity is reduced by one-third. Seeing the level of these living entities the process to go back to the spiritual world is made easier than that in Satya-yuga where they had to perform austerities for thousands of years.Those who are too dull and do not go back in the Treta are again given birth in the Dvapara-yuga where the recommended process to attain self-realization is made much easier.

But those who fail to go back even in Dvapara-yuga are the worst of the lot. They come in Kali-yuga. Therefore, this age of Kali-yuga is described as the most sinful where the people are unfortunate, unintelligent, grossly foolish and always disturbed. Therefore,  the process to go back home back to godhead has been made the easiest by the Supreme Lord i.e.simply by chanting God’s holy names (Hare Krishna Hare Krishna Krishna Krishna Hare Hare, Hare Rama Hare Rama Rama Rama Hare Hare), one can obtain all the results and more very easily that were obtained by severe austerities in Satya-yuga, Yajna in Treta-yuga and elaborate deity worship in Dvapara-yuga.

But even in Kali-yuga there are some who are very very demoniac and sinful. So the Lord personally comes to destroy them and create the golden age of Satya-yuga again.