Mrikandu was a great rishi. Marudvati was his wife. For a long time they had no children.
The rishi prayed to God Shiva. God Shiva appeared to him, and said, "I am pleased with you, Mrikandu. Tell me, do you want a hundred sons, who will live for a long time, but will all be foolish? Or, do you want one very intelligent son, who will live for only sixteen years?"
The rishi at once said, "God, give me that one intelligent son."
God Shiva said, "Good! You shall have him."
Soon the rishi got a son. He named him Markandeya. The boy grew to be very intelligent and handsome. The rishi initiated him with the sacred thread. Markandeya learnt the Vedas and Sastras,easily. Everyone liked him.

As the boy was getting on to be sixteen, Rishi Mrikandu became sadder and sadder. One day Markandeya asked his father: "Father, why do you look so sad?"
The rishi said, "Son! What shall I say? When God Shiva gave you to me, he said you would live only sixteen years. You are now about to reach that age. How can your mother and I bear to lose you as we will at the end of this year?"
Markandeya said, "Father! Is that the reason? God Shiva is very kind to His devotees. You yourself told me that. He has saved many from death before. I have read about it in the Puranas. I shall therefore worship God Shiva day and night from today. I am sure, He will save -me too! "
Rishi Mrikandu was very happy to hear his son say this. He blessed his son.
Markandeya built a Shiva-Linga at a spot on the sea-shore. He started worshiping Shiva morning, noon and night continuously chanting OM NAMAH SHIVAYA! On the last day, Markandeya was about to sing bhajans, when Yama, the God of Death, came to him. Yama rode on a buffalo. He held a noose in his hand. He spoke to Markandeya, "Stop your chanting, you boy! Your life in this world is over. Be ready to die."
Markandeya was not afraid. He clung to the Shiva-Linga as one clings to one's mother and chanted loudly OM NAMAH SHIVAYA!.
Yama threw his noose round the boy's neck, and pulled him along with the Shiva- Linga.
Then the Shiva-Linga burst open and God Shiva came out of it, and said, "Yama, go away! Don't touch this boy. He is my beloved devotee. He will live for ever!"
Yama went away crest-fallen. Markandeya then prayed to God Shiva more fervently than ever. This prayer (CHANDRA SHEKHARA ASTAKAM) says at the end of each line, "What can Death do to me, when I am surrendering to Lord Shiva by constantly chanting HIS name? " Many people recite this prayer even now and believe it to enhance long life for their kids and Good health.
Markandeya came home, and fell at the feet of his parents. They embraced him, and wept with joy.
Markandeya became a great rishi, and lived very long.

Goddess Durga is the mother of the universe (Jagan matha) and believed to be the power behind the work of creation, preservation, and destruction of the world. There are many incarnations of Durga: Kali, Bhagvati, Bhavani, Ambika, Lalita, Gauri, Kandalini, Java, Rajeswari, etc. Bhavani is the lovable form and Durga is said to be the ferocious form (impossible to conquer). Like Lord Shiva, Mother Durga is also referred to as "Triyambake" meaning the three eyed Goddess. The left eye represents desire (the moon), the right eye represents action (the sun), and the central eye knowledge (fire).

Among all the names,  “Durga” is said to be the greatest and most effective. The two roots in the word – “DuH” and “Ga”, which mean impossible/extremely difficult and go/reach respectively. Here is a story on how Mother  was named Durga:-

There was once a demon by the name Durgaman. He got a boon to attain the magical powers and manthras from all the rishis. Because of this boon, Durgaman became very powerful and because of his powers, the rishis forgot their manthras and rituals. Because rituals and prayers were not conducted Devas lost their strength. Rains failed and the rivers and wells dried up. There was famine everywhere. Devas and rishis prayed to Jagan Matha for help. Jagan Matha appeared before rishis. As she appeared in a form with multiple eyes she was named "Sathashi". She also got a name "Sakhambari", as she appeared with flowers, spinach and vegetables in her hand. Jagan Matha protected the devas and rishis and made them strong. Durgaman saw this and started a war with Devi. Devi created a protective enclosure of Agni for devas and rishis to protect them. The devas and rishis remained safely in Devi's protection while She fought with Durgaman and killed him. All the magical powers of Durgaman left him in the form of a fire and joined Devi. She was hence called "Sarva ManthraMayee". Since she killed Durgaman she was also called "Durga".

 “Durga” means impossible to reach/conquer/surpass. There is no way to reach Her except with Her grace, which can be achieved by constant chanting of Her name with devotion. It is said that by constant chant of Mother Durga, we will not have any lows or disturbances in life. Continuous chanting of this name is said to ensure bhava tarana (help us cross the ocean of births and deaths).