This day is part of Golden Week and it's to commemorate an event that happened on May 3, 1947, when the old constitution was replaced by the new constitution. The old constitution gave power to the emperor and the new constitution gave power to the people.
Constitution Memorial Day is a national public holiday.
In 1947 the new constitution replaced the Meiji Constitution. The new constitution was modeled after the American and British constitutions which gave power to the people much like a democratic society.