It was destroyed during the First Rebellion when the united districts of Panem rebelled against the Capitol's oppressive rule.
Near the end of the war, District 13 trained nuclear missiles on the
Capitol, hoping to destroy the Capitol even if the result was mutually
assured destruction. However, District 13 set up a secret deal with
the Capitol - they would withdraw their forces from the war and
present the illusion that Capitol bombers equipped with Toxic bombs
destroyed District 13. 13 withdrew and rebuilt their district
underground. The Capitol's bombers then destroyed the district on the
surface. Without 13's aid, the remaining rebel forces were put down by
the Capitol.
The Hunger Games commemorate the Capitol's victory in this war and serve to remind the citizens of Panem of the futility of rebellion.
Sources:
http://thehungergames.wikia.com/wiki/Dark_Days