Its is the most important square in Greece and certainly in Athens.
Syntagma Sq (which translates to Constitution Sq in English) is also close (walking distance) to the major attraction like the Acropolis, National Gardens, Temple of Olympian Zeus, Hadrian's Arch, the Choreographic monument of Lysicrates, the Plaka, and the ancient Roman and Greek Agoras.
Syntagma Square is the administrative heart of Greece and the symbolic center of Athens. The big building that you see taking up a corner of the National Gardens is the Parliament or Vouli Building. Just below the Vouli building and part of it is the Tomb of the Unknown Soldier.
Every Sunday at 11 am the Guard at the Tomb of the Unknown Soldier changes and its a free show worth seeing. Arrive 20 minutes early to get a standing room only place from which to view the proceedings. Pet the inevitable pack of Athenian dogs that arrive right on time to see the show.
If you cant make the Sunday show, lesser guard changing takes place regularly on the hour, 24/7/365.
Here, on September 3d, 1843, and at odds with the wishes of the current sovereigns, Otto and Amelia, the Constitution or Syntagma was proclaimed (bloodlessly) from the balcony of the Vouli Building by General Kallergis and his adherents. Up until that point the square was known as the Garden of the Muses. The beautiful period designed Gardens still remain, flourish and should be walked without fail. There are many conveniences to be found here such as banks, stores and restaurants.
Visitors have to come to Syntagma Sq at least once if they want to say that they have seen Athens.