It is the festival of celebration of nine days in India. After the ninth day, the tenth day is called as Vijayadhashami. Here vijaya doesnt mean victory. It is the breaking of the shackles of the mind and the attainment of complete freedom.
Navam also means new. We wash away all the papas in our mind and during this time and we get a new birth. During the first three days of the festival, Durga is worshiped. She is the fierce aspect of god. We worship her to remove our desires,fighting against our own anger and all the negatives within the mind. The sword in the hand of Durga is the symbol of vairagya [dispassion]. It is the sword of knowledge. The intense desire to know God is viaragya. By worshiping Durga, we are trying to awake our indwelling shakti.