He was born in Kalady, a small village in Kerala, India. He was born to a Nambuthiri brahmin couple, Sivaguru and Aryamba.
The traditional sources of accounts of Sankara's life are from the Sankara Vijayams. These are hagiographies on the life of Sankara. The most important among them are the MadhavIya Sankaravijaya, the AnandagirIya Sankaravijaya, cidvilAsIya Sankaravijaya and keralIya Sankaravijaya.
What follows is the generally accepted biography of Sankara.
Sankara's parents had no child for a long time, and prayed at Vadakkumnathan (vRashAcala) temple in Thrissur, Kerala. Legend has it that the Lord Siva appeared before the devout couple and offered them a choice: a mediocre son who will live a long life, or an extraordinary son who will not live long. The couple chose the latter. The son was named Sankara, in honour of the Lord Siva.
Sivaguru passed away in Sankara's infancy. The child showed remarkable scholarship, and is said to have mastered the four Vedas by the age of eight. Following the common practice, Sankara stayed at a teacher's house. On one occasion, while begging for alms, he came upon a woman with nothing but one dried amlaka fruit, which she offered to him with devotion. Moved by her piety, he composed the Kanaka Dhara Stotram. On completion of the stotram, golden amlaka fruits were showered upon the woman by the Goddess Lakshmi. On another occasion, Sankara was bathing in the river, when a crocodile caught him. He asked his mother permission to adopt Sanyasa (the ascetic life), and when his mother relented, the crocodile released him. This is the legend of Sankara's adoption of Samnyasa.
Sankara then left Kerala and travelled thoroughout India. When he reached the banks of the river Narmada, he met Govinda Bhagavatpada, the disciple of the Advaitin Gaudapada. As his disciple, Sankara was initiated.
Sankara travelled extensively, meanwhile writing commentaries on the Upanishads, Vishnu sahasranama, and the Bhagavad Gita. He engaged in a series of debates with Buddhist scholars, and with scholars of the Purva Mimamsa school, which helped in cementing the spiritual ascendancy of Sankara. One of the most famous of these debates was with Mandana Misra.
Yet, his most famous encounter was not with the famed ritualist Mandana Misra but with a lowly untouchable. On his way to the Viswanath temple in Kashi, he came upon an untouchable and his dog. When asked to move aside by Sankara's disciples, the untouchable asked: "Do you wish that I move my soul,the atman and ever lasting, or this body made of clay?" Seeing the untouchable as none other than the Lord, Sankara prostrated before Ishwara, composing five slokas (Manisha Panchakam).
Sankara is believed to have attained the Sarvajnapitha in Kashmir. After a while, he withdrew to Kedarnath and attained Samadhi at the age of 32. The Kamakshi Amman temple at Kanchipuram also has a brindavanam where he is believed to have attained siddhi. (A variant tradition expounded by keralIya Sankaravijaya places his place of death as Vadakkumnathan (vRashAcala) temple in Thrissur, Kerala).
Shri Shankaracharya, Adhi Shankaracharya, or Adi Shankara ("the first Shankara" in his lineage), reverentially called Bhagavatpada Acharya (the teacher at the feet of Lord), Shankara (approximately 509- 477 BC, some claim 788-820 CE)  (http://www.easterntradition.org/original%20sankaracarya.pdf) was the most famous Advaita philosopher who had a profound influence on the growth of Hinduism through his non-dualistic philosophy. He advocated the greatness and importance of the important Hindu scriptures, the Vedas (most particularly on the Upanishads, also known as Vedanta), spoke to a spirituality founded on reason and without dogma or ritualism, and gave new life to Hinduism at a time when Buddhism and Jainism was gaining popularity.