In 1999, India and Pakistan went to the Kargil War with each other and India as usual, India defeated Pakistan. The war was fought in the months of May and July and around 527 Indian soldiers were martyred and 1363 were injured in it. From that side, more than 3000 soldiers were killed. Pakistan, however, show the number to be 357 only.
The war took place at the highest altitude of the world and Indian soldiers forced Pakistanis to go back to their side of the border.
So it is to commemorate the contribution and bravery of these martyrs and soldiers that Kargil Vijay Diwas is celebrated. Many nations supported India in defeating Pakistan in this Kargil War. The war is also famous by the name of Operation Vijay and hence the day is popularly celebrated as Vijay Diwas (the day of victory).