Vijayadashami also known as Dussehra is a festival celebrated by all Indians though it's a Hindu festival. This occasion signifies as victory of Good over Evil and people celebrate to bring new things their life. It is celebrated on the tenth day of the bright fortnight Shukla Paksha of the Hindu autumn month of Ashvin and is the grand culmination of the 10-day annual Navaratri festival. Few significant Hindu mythological related short stories are mentioned below to bring out the importance of this festival.
Victory of Lord Sri Ramachandra over Demon Ravana
Sri Rama had performed "Chandi Hom" and invoked the blessings of Durga to kill Ravana. Durga blessed Sri Rama with the secret to kill Ravana. Ravana was defeated in his own kingdom of Lanka by Sri Rama and the Vanarsena. Sri Rama with Sita & Laxman returned victorious to their kingdom of Ayodhya on auspicious day of Ashwin Shukla Dashami as per Hindu calendar. This victory of Rama is since then celebrated as "Vijaya Dashami" which means victory on tenth day.
This event is also celebrated with another Hindu mythological story of Maa Durga victory over Demon Mahishasur Rakshas. Some of the Aasuras (Demons) were very powerful and ambitious, and continually tried to defeat Gods and capture the Heaven. One such Aasura called Mahishasur, who looked like a buffalo, grew very powerful & created havoc on the earth. Under his leadership the Aasuras even defeated the Devas (Gods), all of whom were powerless including Brahma, Vishnu & Mahesh along with other Gods. Finally, when the world was getting crushed under Mahishasura's tyranny, the Devas came together & contributed their individual energy to form "Shakti" a single mass of incandescent energy to fight & kill Demon Mahishasur.
End of Agyatwas of PANDAVAS
In Dwapar Yuga, after Pandavas lost to Kauravas in the game of Dice, they had to proceed to 12 years of "Vanwas" (exile to forest) followed by one year of Agyatwas. Pandavas spent 12 years in forest and hid their weapons in a hole on a "Shami" tree before entering the Kingdom of Virat to complete the last one year of Agyatwas. After the completion of that year on Vijayadashmi they took the weapons from the Shami tree, declared their true identity & defeated Kauravas, who had attacked King Virat to steal his cattle wealth.
Since that day the exchange of Shami leaves on Dussehra day became symbol of goodwill and victory. Hence on Dussehra Shami Tree & the weapons are worshipped on this occasion by all Hindus.