Rishi Mrikandu and Marudmati his wife had no child and hence were very sad. They started praying to Lord Shiva and after long tapashya (penance) Shiva appeared in front of them granting them a boon of a son. But the catch was that their son would either be very intellegent having a shorter lifespan or will live long and will not be so intellegent. Mrikandu and his wife choose the 'intellegent son' option and Markandeya was born.

Markandeya turned out to be a strong devotee of Lord Shiva. As he grew up as a teenager his parents started worring for this life. Upon seeing Rishi Mrikandu and Marudmati depressed Markandeya insisted on knowing the reason and the truth was revealed. Markandeya didn't wanted to die at a young age leaving his parents alone and sad and hence started his tapashya offering prayers to Lorad Shiva in front of a Shiva Linga. This is when it is said that Mrityunjaya Mantra was believed to be created by Markandeya to please Lord Shiva.

When Yamraj send his messenger to take Markandeya's life, he was in deep meditation and the messenger had to return empty handed. Seeing this Yamraj himself came down to earth to take Markandeya who immediately embraced the Shiv Linga in front of him asking for mercy. Yamraj had to complete his duty and hence threw his noose on Markandeya which accidentally fell around Shiva Linga. This made Lord Shiva very angry and he killed Lord Yamaraj immediately.
All Gods gathered together and pleaded to Lord Shiav to revive Yamaraj as death of Lord Yama would disrupt the balance of the entire universe. Lord Shiva agreed and brought Yamaraj back to life but on a condition of letting Markandeya live to which all Gods agreed.