Vijayadashami (Bengali: বিজয়াদশমী, Kannada: ವಿಜಯದಶಮಿ, Malayalam: വിജയദശമി, Marathi: विजयादशमी, Nepali: विजया दशमी, Oriya: ବିଜୟାଦଶମୀ, Tamil: விஜயதசமி, Telugu: విజయదశమి, Konkani: दसरो, Punjabi: ਦਸੇਰਾ) also known as Dashahara, Dussehra, Dashain (in Nepal), Navratri or Durgotsav is one of the most important Hindu festivals celebrated in various forms, across India, Nepal and Bangladesh.
The name Dussehra is derived from Sanskrit Dasha-hara literally means remover of ten referring to Lord Rama’s victory over the ten-headed demon king Ravana. The day also marks the victory of Goddess Durga over the demons Mahishasur. The name Vijayadashami is also derived from the Sanskrit words “Vijaya-dashmi” literally meaning the victory on the dashmi (Dashmi being the tenth lunar day of the Hindu calendar month). Significance
As the name suggests Vijayadashmi or Dussehra is celebrated on the tenth day of the month of Ashwin according to the Hindu lunisolar calendar which corresponds to September or October of the Gregorian calendar. The first nine days are celebrated as Maha Navratri(Devnagari: नवरात्रि, ‘nine nights’) or Sharada Navratri (the most important Navratri) and culminates on the tenth day as Dasara.
In India, the harvest season begins at this time and so the Mother Goddess is invoked to start the new harvest season and reactivate the vigor and fertility of the soil. This is done through religious performances and rituals which are thought to invoke cosmic forces that rejuvenate the soil. Many people of the Hindu faith observe through social gatherings and food offerings to the gods at home and in temples throughout Nepal and India. 
Victory of God Rama over Ravana
See also: Ramayana, Shri Rama, and Ravana
Effigy of Ravana burns
On this day in the Treta Yug, Rama, also called Shri Ram, the seventh avatar of Vishnu, killed the great demon Ravana who had abducted Rama’s wife Sita to his kingdom of Lanka. Rama, his brother Lakshmana, their follower Hanuman and an army of monkeys fought a great battle to rescue Sita. The entire narrative is recorded in the epic Ramayana, a Hindu scripture.
Rama had performed “Chandi Homa” and invoked the blessings of Durga, who blessed Rama with secret knowledge of the way to kill Ravana. On the day of Ashvin Shukla Dashami, Rama’s party found Sita and defeated Ravana. Thus it is termed as Vijaya Dashami. Based on the inferences from Valmiki’s Ramayana, Kalidas’s Raghuvans, Tulsidas’s Ram Charit Manas, and Keshavdas’s Ram Chandra Yas Chandrika as well as common perception in India, Rama, Sita, and of Lakshmana returned to Ayodhya on the 30th day of Ashvin (19–20 days after Vijayadashmi). To mark the return of Lord Rama, in the evening, the residents of Ayodhya lit their city with millions of earthen lamps (called Deepak). Since then, this day is celebrated in India as Deepawali or Diwali.
Many people perform “Aditya Homa” as a “Shanti Yagna” and recite Sundara Kanda of Srimad Ramayana for 5 days. These Yagna performances are thought to create powerful agents in the atmosphere surrounding the house that will keep the household environment clean and healthy. These rituals are intended to rid the household of the ten bad qualities, which are represented by 10 heads of Ravana as follows: Kama vasana (Lust)