Navaratri is celebrated four times a year. They are Ashada Navaratri, the Sharada Navaratri, the Maha Navaratri and the Vasantha Navaratri. Of these, the Sharada Navaratri of the month of Puratashi and the Vasantha Navaratri of the Vasantha kala are very important. If you refer to the agni purana, then it is said that the Puratashi and Panguni (in Tamil months) i.e. Asvin and Chaitra are like the two jaws of Lord Yama. If one wants to escape the mouth of Yama, then one should celebrate Navaratri on these two occasions. A similar analogy is presented in the devi bhagavatam. Devi bhagavatam also talks in detail on how one should observe fasts, and how one should meditate/work on these days. According to legend, when the demon king Mahishasura became invincible after getting boons from brahma and tormented all the three worlds and the Devatas and the Trinity were helpless, Lord Vishnu prayed Mother Shakti and she manifested in the form of Durga. All the Devatas prayed her and presented her with various ornaments and their weapons. During her war with Mahishasura, Durga created Kali, Chandi and Chamundi out of Herself and destroyed the demon king Mahishasura.
It is stated that Durga sat on the tip of a needle for nine days, doing a severe penance to destroy the evil Asura Mahisha. On the first three days, she meditated as Herself, the next three days as Mahalakshmi and the last three days as Sarasvati. This signifies progression from tamsik, to rajasik to satvik and eventually obtaining liberation. The tenth day during Sharada Navaratri is called vijayadashami to signify the victory on the day of dashami. It is, however, a long tradition that one reads the devi-bhagavatam or the devi mahatmyam (Durga saptashati, 700 verses on Durga) during this period. Devi bhagavatam notes that Rama meditated and fasted for nine days after Sita was kidnapped by Ravana.