I must confess, I had never heard of this holiday until today. It showed up on my calendar and I just had to do some investigating to see what it was and why we celebrate it.
As it turns out, it is also called Constitution Day and it's celebrated as a way to acknowledge the ratification of the U. S. Constitution. It started out in the 1940's by congress as "I am an American" Day.
A law was passed by the late Senator Bryd (I believe around 2007) stating that all government-funded institutions had to teach their citizens about the constitution, their responsibilities and opportunities as citizens on both the state and federal levels.
If it's been awhile since you've read the Constitution, here's the link.
Whether you call it Citizenship Day or Constitution Day, it is set aside to celebrate and honor our United States Constitution.