Disclaimer: Kali Purusha is not to be confused with Kali Ma (i.e., Goddess Kali, whose name is pronounced 'Kaa-lee', whereas Kali Purusha is pronounced ‘Kuh-lee’).
Om Namo Bhagavate Vasudevaya!
Kali Purusha is the personality that is the embodiment of all negativity in Kali-yuga (i.e., the age of quarrel) and can loosely be termed as the Vedic equivalent of the personality of Satan in the Abrahamic traditions.
Kali Purusha is described in the Srimad Bhagavatam as the son of anger and envy, the grandson of cunningness and greed, the great-grandson of pride and illusion, and the great-great-grandson of sin and falsehood.
mṛṣādharmasya bhāryāsīd dambhaṁ māyāṁ ca śatru-han asūta mithunaṁ tat tu nirṛtir jagṛhe ’prajaḥ tayoḥ samabhaval lobho nikṛtiś ca mahā-mate tābhyāṁ krodhaś ca hiṁsā ca yad duruktiḥ svasā kaliḥ
Translation:
“Another son of Lord Brahmā was Irreligion, whose wife’s name was Falsity. From their combination were born two demons named Dambha, or Bluffing, and Māyā, or Cheating. These two demons were taken by a demon named Nirṛti, who had no children. Maitreya told Vidura: O great soul, from Dambha and Māyā were born Greed and Nikṛti, or Cunning. From their combination came children named Krodha [Anger] and Hiṁsā [Envy], and from their combination were born Kali and his sister Durukti (Harsh Speech).” - Srimad Bhagavatam 4.8.2–3
It is said once Lord Krishna’s leela was finished, Kali Purusha began to reign and increase the influence of adharma and paap (i.e., unrighteousness and sin) in ignorant individuals who lack spiritual consciousness and are attracted to materialism.
yasminn ahani yarhy eva bhagavān utsasarja gām tadaivehānuvṛtto ’sāv adharma-prabhavaḥ kaliḥ
nānudveṣṭi kaliṁ samrāṭ sāraṅga iva sāra-bhuk kuśalāny āśu siddhyanti netarāṇi kṛtāni yat
kiṁ nu bāleṣu śūreṇa kalinā dhīra-bhīruṇā apramattaḥ pramatteṣu yo vṛko nṛṣu vartateTranslation:
“The very day and moment the Personality of Godhead, Lord Śrī Kṛṣṇa, left this earth, the personality of Kali, who promotes all kinds of irreligious activities, came into this world. Mahārāja Parīkṣit was a realist, like the bees who only accept the essence [of a flower]. He knew perfectly well that in this Age of Kali, auspicious things produce good effects immediately, whereas inauspicious acts must be actually performed [to render effects]. So he was never envious of the personality of Kali. Mahārāja Parīkṣit considered that less intelligent men might find the personality of Kali to be very powerful, but that those who are self-controlled would have nothing to fear. The King was powerful like a tiger and took care for the foolish, careless persons.” - Srimad Bhagavatam 1.18.5–8
To prevent Pariksit Maharaja from killing him, Kali Purusha agreed that he would only reside in places where unrighteous activities were performed.
sūta uvāca abhyarthitas tadā tasmai sthānāni kalaye dadau dyūtaṁ pānaṁ striyaḥ sūnā yatrādharmaś catur-vidhaḥ
Translation:
“Sūta Gosvāmī said: Mahārāja Parīkṣit, thus being petitioned by the personality of Kali, gave him permission to reside in places where gambling, drinking, prostitution and animal slaughter were performed.” - Srimad Bhagavatam 1.17.38
He was not destined to be killed by Pariksit Maharaja because it is prophesied that Lord Vishnu, as His incarnation of Lord Kalki, will kill all adharmic personalities, including Kali Purusha, and end Kali-yuga:
aśvam āśu-gam āruhya devadattaṁ jagat-patiḥ asināsādhu-damanam aṣṭaiśvarya-guṇānvitaḥ
vicarann āśunā kṣauṇyāṁ hayenāpratima-dyutiḥ nṛpa-liṅga-cchado dasyūn koṭiśo nihaniṣyatiTranslation:
“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 opulences and eight special qualities of Godhead. Displaying His unequaled effulgence and riding with great speed, He will kill by the millions those thieves who have dared dress as kings.” - Srimad Bhagavatam 12.2.19–20
This is stated by Lord Vishnu Himself in the Kalki Purana to the devatas:
"After hearing everything that the demigods had to say regarding the situation on earth, the lotus-eyed Lord Hari said: O Brahma, rest assured that I will soon descend to the earth and appear in the village known as Shambhala. I will take birth in the house of a Brahmana named Vishnuyasha, from the womb of his wife, Sumati. My mission will be to eliminate the wicked Kali and his influence with the help of My four brothers. O devatas, your expansions should also take birth on the earth to assist Me in My mission. My consort, the beloved lotus-eyed Kamala-devi, will also appear on the earth, having the name Padma. She will be born from the womb of Kaumudi, the wife of Brihadratha, the king of Simhala. O demigods, you should not delay. By your plenary portions, take birth on the earth. Later on, I will entrust the responsibility for ruling the earth to two powerful kings named Maru and Devapi. I will then again establish Satya-yuga, and thus reinstate the principles of religion as they were before. Rest assured that I will return to Vaikuntha only after destroying the poisonous snake, Kali." - Kalki Purana (2.4–8)
Hare Krishna