Navratri is divided into sets of three days to adore 3 different aspects of the supreme goddess or goddesses.
First 3 days:
The goddess is separated a spiritual force called Durga also known as Kali in order to destroy all our evil and grant boons.
Second 3 days:
The Mother is adored as a giver of spiritual wealth, Lakshmi, who is considered to have the power of bestowing on Her devotees inexhaustible wealth, as She is the goddess of wealth.
Final 3 days:
The final set of three days is spent in worshiping the goddess of wisdom, Saraswati. In order to have all-round success in life, believers seek the blessings of all three aspects of the divine femininity, hence the nine nights of worship.
Happy Navratri!!