Navaratri is a Hindu holiday in honor of Shakti, the divine feminine energy. Navaratri takes place during the Indian month of Aashwayuja, generally falling in October, during the bright half of the moon. There are many goddesses in Hinduism, each one representing a different aspect of the divine. Navaratri is a celebration that specifically honors Durga, Lakshmi, and Saraswati. The celebration lasts nine days.
On the first three days, Shakti is adored as supreme power and force, as Durga the Terrible to destroy one's all impurities, vices, and defects.
Durga is the destroyer, the warrior. Riding on the back of a lion, Durga destroys impurity and vice. Spiritually, she destroys the illusions and diversions that distract one from the truth.
The next three days are dedicated to Lakshmi. Lakshmi is the goddess of abundance and virtue. The positive virtues that she embodies replace the negative qualities Durga destroys.
The last three days are dedicated to Saraswati, the embodiment of divine wisdom. Saraswati bestows the wisdom of the Absolute.
The tenth day, celebrated after the nine days of Navaratri is called Vijaya Dasami. On the spiritual journey, Vijaya Dasami marks the victory of the souls journey through the world. With the grace of Durga, Lakshmi, and Saraswati, the soul attains liberation.
The tenth day is also known as Dusshara, and is celebrated as the day Lord Rama cut off the ten heads of the demon Ravana.
Thanks to Rischi for encouraging me to elaborate, and providing some additional details.