Maa Durga is worshipped in her nine forms during Navratri. The sixth form of the Goddess is Maa Katyayani and she is worshipped on Shashthi (sixth day) of Durga Puja. There is a story behind this name.
There was a famous Maharshi by the name of Kata. His daughter was Rishi Katya. The famous Katyayan was born in Rishi Katya's tribe. He worshipped Maa Bhagwati Paramba and underwent severe penance for many years. He wished that Maa Bhagwati should be born in his house as his daughter. Later, Maa Bhagwati accepted his prayer.
After some years, when the autocracy of demon Mahisasura became acute on earth, Lord Brahma, Vishnu and Maheshwar combined their divine rays to create a goddess. Maharshi Katyayan first worshipped that goddess and she fulfilled his wish. This way she got the name Katyayani.
Maa Katyayani is the unfailing fruitfulness. Brajgopis used to worship Maa Katyayani on the banks of the Yamuna to get Lord Krishna as their husband.
Her devotees become the possessors of great powers and achieve heights of success as they remain constantly blessed by Maa Katyayani. Therefore, one should bow down before the Goddess and always remain engrossed in her worship.