Here are some key things.
Goddesses Durga have been historically worshiped in mainly 9 forms on these 9 days of Navratris. Nav-ratri means Nav ratris, nav means 9, ratris means nights. Here is a quick brief on the reason of praying her during this time.
These 9 days she fought with demons and 10th days victory was declared. These days are celebrated with zeal.
After these 9 days and nights. Vijayadashmi is celebrated. Other Gods gave all their powers for Goddesses to fight the devil Mahishasur to save heavens. On this 10 th day of fight Mahishasur devil was killed. This day is celebrated with glamour. On the same day Dussehra is also celebrated.
Here is it:
She took the form of Kali to kill the demons. Kal also means Time, in a language.