Parikshita is the son of Uttara, the Matsya princess and Abhimanyu, the Vrishni son of Arjuna. He is born only after the end of the war.
Uttara is carrying their son in her womb when Abhimanyu is mercilessly and unfairly slain by the Kauravas. Later, Ashwathama attempts to kill the unborn child and his mother by directing the brahmastra towards her tent off the battlefields. She is saved by Lord Krishna, who was also the maternal uncle of Abhimanyu (Arjuna's wife Subhadra was the sister of Lord Krishna and mother of Abhimanyu.)
The chief priest Dhaumya predicts to king Yudhisthira after Parikshita's birth that he will be a great devotee of the Supreme Lord Vishnu, and since he was saved by the Lord Krishna, he will be known as Vishnurata (One who is always protected by the Lord).
Dhaumya Rishi predicts that Parikshita would be ever-devoted to virtue, religious principles and the truth and would be a wise monarch, exactly as Ikshvaku and Rama of Ayodhya. He would be as exemplary a warrior as Arjuna, his own grandfather, and would expand the fame of his family.
He is given the name Parikshita as he would search and test for the Supreme Lord, whom he had witnessed as an unborn child, across the world and within every human being.
Upon the commencement of the Kali yuga, the dark age of sin, and the departure of Krishna Avatara from the world, the five Pandava brothers retire. Young Parikshita is duly invested as king, with Kripa as his counselor. He performed three aswamedha yajnas under the guidance of Kripa.
Once Parikshita went hunting in the forest. Kali, the embodiment of Kali Yuga, appeared before him and asked permission to enter his kingdom, which the king denied. Upon insisting, Parikshita allowed him four places to reside: where there is gambling, alcohol consumption, prostitution and gold. Kali smartly entered into Parikshita's golden crown and spoiled his thoughts.
Parikshita entered into a sage Shringi's hut as he was thirsty. He found the sage in deep meditation. He bowed to him several times but as their was no response he took a dead snake and threw it around the sage's neck. Later when the sage's son heard of this incident and cursed the king to die of a snake bite on the 7th day.
On hearing this, the king forswore the throne for his son Janamejaya and spent his last 7 days listening to the discourses of Sage Sukadeva on Bhagavata. As prophesied, the snake king Takshaka bit Parikshita, who left his mortal remains behind and attained salvation.
Other thesis say that Kali had entered the gold and thus creating man's desire for gold. Parikshit had gone hunting into the forest. He stops at one point and gets into the lake for a bath. He removes his crown and keeps it on the bank of river. Takshaka, a naga king sees the golden crown and desires to get it. He steals the crown, but he was got by Parikshita guards. Parikshita jails him. On his release Takshaka avenges Parikshita and kills him mercilessly.
On hearing this, Parikshita's son Janamejaya vows to kill all the naga in a week. Janamejaya starts his killing spree of naga. He brutally murders Takshaka. Asthika, a close friend of Janamejaya, minister and a philosopher comes to know of Janamajaya's act and stops him.