Chir means for a very long time or for ever, and Jeevee means to live, so Chir-jeevee means "who lives forever". For some discussion on Chiranjeev see the following sites -- http://3ws.veda.harekrsna.cz/encyclopedia/general.htm.

The Vishnu Puraan says that the next Ved Vyaas will be Drone's son Ashwatthaamaa. As you may know from the MBH, Ashwatthaamaa is immortal. http://3ws.dharmakshetra.com/literature/puranas/VISHNU.htm. Here on this site , much material is there regarding Ashwatthaamaa:  http://3ws.factbites.com/topics/Ashwatthama.

Also see this site, a good summarization of war chapters: http://3ws.warriormonks.com/kurukshetra/kurukshetra.html. MBH will not tell Whys and Hows about these Chiranjeevee people, we have to search this in related Puraan.

There are seven Chiranjeevee in Hindu mythology -

(1) Ashwatthaamaa
Son of Drone and Kripee. He was a mighty warrior. He had even learnt the art of invoking Brahm Astra, but his father did not teach him to bring it back because of his ruthlessness. When he used it first at Arjun, he could not call it back and had to divert it at Uttaraa. Arjun took his Mani (jewel) from his forehead and Krishn cursed him to live forever, the wound festering, never to heal. This happened because of unethical behavior.

(2) Parashuraam
Avataar of Vishnu, son of Rishi Jamadagni and Renukaa. Parshuraam was the master of martial arts. No one could beat him whether it was Astra, Shastra or Divine weapons. he had no worldly ambition. He never hesitated to admit a mistake. He asked forgiveness of Raam and Lakshman at Seetaa Swayamvar. He symbolizes excellence and strength, tempered by humility.

(3) Hanumaan
Avataar of Shiv, son of Vaayu Dev and Anjanee Devee. Hanumaan exemplifies selflessness, courage, devotion, energy, strength and righteous conduct. He stand for the potential which is in all of us. Seetaa gave this boon to him to be ever youthful, energetic, and immortal.

(4) Ved-Vyaas
Avataar of Vishnu, son of Rishi Paraashar and Matsyagandhaa (Satyavatee). A Kathaa Vaachak (teller) has to ascend Vyaas Peeth - blessed by the immortal Vyaas. He represents the continuity of erudition, scholarship and the apotheosis of the writer as the ultimate visionary.

(5) Vibheeshan
Son of Maharshi Vishravaa and Kaikasee, brother of Raavan and Kumbhkarn. Vibheeshan had unshakable faith in what he believed. He was a fearless counselor of righteousness even when all around him were under peer pressure.

(6) Kripaachaarya
Son of Maharshi Sharadwaan and Apsaraa Urvashee. Kripaachaarya was an extraordinary teacher. To him all pupils were the same. While a Guru like Dronaachaarya favored Arjun and sacrificed equally, if not more promising students like Eklavya and Karn.

(7) Daitya Raaj Bali
Son of Virochan and Devee, grandson of Prahlaad. Bali was immortalized because Vishnu had to humble Himself as Vaaman to conquer him. He stands out for his valor and charity - two great eternal qualities. Knowingly fully well about Vaaman he gave everything, including his body, to Him. So his grace is revered.

These seven immortals exemplify certain basic truths, laws and standards of ethical behavior which transcend time, space and generation. They are universal and immutable. Their immortality is therefore not mere deathlessness - it is more the immortalizing of each Divine principle they stood for, and upheld even in the situation of adversity and pressure.

(8) Maarkandeya
Son of Mrikand Muni. He was given only 16 years of life but by his devotion to Shiv he attained immortality. Once he saw Pralaya (Deluge) as a boon from Bhagavaan.

(9) Kaagbhushundi Jee
He is also Chiranjeevee and a very special one. Most people have only one Kalp age, but he has been living for the last 27 Kalp - so says Kaagbhushundi Jee himself in Tulasee's Raam Charit Maanas, 7/15.

Others are -
(10) Naarad Jee,
(11) Takshak Naag...