Constitution Day commemorates the approval of a new constitution in Spain that originally happened on December 6, 1978. It is always held on December 6th.
In the days leading to the actual holiday students will be taught about Spain's history as a monarchy into democracy. Then on the actual date there is a cocktail party in the parliament building and many just hang out to enjoy the day off.
Francisco Franco was the head ruler of the country in 1939 until his death when Spain realized they needed a new constitution and government policy. So the parliament drew up a new constitution and had the public vote for it to which 88% of the public agreed with it. Therefore making it an actual constitution in December 6, 1978.