The Apocalyptic Horse Rider - Appearance of Kalki Avatar
"Thereafter, at the conjunction of the two yugas, the Lord of creation will take His birth as the Kalki incarnation and become the son of Visnu Yasa. At this time the rulers of the earth will have degenerated into plunderers." [SB 1.3.25] 0 Kesava, O Hari, who have assumed the form of Kalki! You appear like a comet and carry a terrifying sword for bringing about the annihilation of the wicked barbarian men at the end of the Kali-yuga. [ Sri Dasavatara Stotra, 10th Sloka]

"Lord Kalki, the Lord of the universe, riding His swift horse Devadatta and, sword in hand, will travel over the earth exhibiting His eight mystic powers and eight special qualities of Godhead. Displaying His unequalled effulgence and riding with great speed, He will kill by the millions those thieves and rogues who have dared dress as kings." [SB. ]

The Appearance of Lord Kalki, the Avatar or incarnation of Godhead, is foretold in the Srimad Bhagavatam 12th Canto and described also in detail in the Brahmanda-purana. Therein it gives predictions as to where he will appear (the village name), who his parents will be, what his mission will be, and when he will appear.

It is described that he will appear at the conjunction of the two yugas, namely at the end of Kali-yuga and the beginning of Satya-yuga. The great cycle of the four yugas, namely Satya, Treta, Dvapara and Kali, rotates like the calendar months. The present age of Kali-yuga lasts 432,000 years, out of which we have passed only 5,000 years after the Battle of Kuruksetra and the end of the regime of King Pariksit. So there are 427,000 years balance yet to be finished, till the advent of Lord Kalki. Therefore at the end of this period, the incarnation of Kalki will take place, as foretold in the Srimad-Bhagavatam. The name of His father, Visnu Yasa, a learned brahmana, and the village Sambhala are also mentioned.

shambhala-grama-mukhyasya brahmanasya mahatmanah bhavane vishnuyashasah kalkih pradurbhavishyati

"Lord Kalki will appear in the home of the most eminent brahmana of Shambhala village, the great soul Vishnuyasha."

ashvam ashu-gam aruhya devadattam jagat-patih asinasadhu-damanam ashtaishvarya-gunanvitah

"Lord Kalki, the Lord of the universe, will mount His swift horse Devadatta and, sword in hand, travel over the earth exhibiting His eight mystic opulence's and eight special qualities of Godhead.

vicarann ashuna kshaunyam hayenapratima-dyutih nripa-linga-cchado dasyun kotisho nihanishyati

"Displaying His unequalled effulgence and riding with great speed, He will kill by the millions those thieves who have dared dress as kings."

atha tesham bhavishyanti manamsi vishadani vai vasudevanga-ragati- punya-gandhanila-sprisham paura-janapadanam vai hatesv akhila-dasyushu

"After all the imposter kings have been killed, the residents of the cities and towns will feel the breezes carrying the most sacred fragrance of the sandalwood paste and other decorations of Lord Kalki, and their minds will thereby become transcendentally pure."

yadavatirno bhagavan kalkir dharma-patir harih kritam bhavishyati tada praja-sutish ca sattviki

"When the Supreme Lord Hari [Krishna] has appeared on earth as Kalki, the maintainer of religion, Satya-yuga [the age of truth] will begin, and human society will bring forth progeny in the mode of goodness."

The mission of Kalki Avatara is to re-establish the religious principles, which have disappeared by the end of Kali Yuga, the iron age of hypocrisy and quarrel.

yada yada hi dharmasya glanir bhavati bharata abhyutthanam adharmasya tadatmanam srijamy aham

"Whenever and wherever there is a decline in religious practice, O descendant of Bharata, and a predominant rise of irreligion--at that time I descend Myself." "In order to deliver the pious and to annihilate the miscreants, as well as to re-establish the principles of religion, I advent Myself millennium after millennium." [BG 4.7-8]

By the End of Kali Yuga, the population of the whole world will be so much reduced to animalism that there will be no more power to understand what is God, or what is spiritualism. And it is already there, the Kali-yuga. It will increase. People will have no power to understand this philosophy, God consciousness. So at that time, when there are no more religious principles, there is no other alternative than to kill them all.

At that time the Kalki avatara will come, and He'll take a sword on the horseback, just like a king send from heaven, He'll simply go on killing all these non-believers, Godless creatures and usher in another Satya-yuga, the golden age of righteousness and truth.
Kalki avatara is the last of the ten major incarnations of Lord Vishnu who will appear in the end of this Kali Yuga to protect religious principles.