Neun (nava) nights (ratri).
Durga, the warlike aspect of Parvati, fought the buffalo demon Mahisha for nine days. On the tenth day she defeated him. This day is Vijaya Dashami, the victorious (vijaya) tenth (dashami) day, also called Dussehra. Another name for the festival is Durga Puja.
Read about the fight here
http://hindumythologyforgennext.blogspot.com/2011/12/goddess-durga-slayer-of-mahisha.html
A lot of information on Navaratri
http://utkarshspeak.blogspot.com/2011/09/navratri.html
http://utkarshspeak.blogspot.com/2010/10/navratri.html
http://utkarshspeak.blogspot.com/2013/10/navratri.html
http://utkarshspeak.blogspot.com/2011/10/navratri-forms-of-goddess.html
http://utkarshspeak.blogspot.com/2011/10/navratri-forms-of-goddess-part-2.html
http://utkarshspeak.blogspot.com/2014/09/worship-of-shakti.html
http://utkarshspeak.blogspot.com/2013/10/durga-puja-and-lord-ram.html
http://utkarshspeak.blogspot.com/2010/10/clay-for-durga-idols.html
http://utkarshspeak.blogspot.com/2013/10/navratri-golu.html
http://utkarshspeak.blogspot.com/2013/10/durga-puja-and-women-folk.html