Those are ceremonial uniforms of the Evzones from the Ottoman Occupation. The tassels symbolize the "tears of the years of oppression."

Quote:

The Evzones, or Evzoni, (Greek: Εύζωνες, Εύζωνοι) is the name of several historical elite light infantry and mountain units of the Greek Army. Today, it refers to the members of the Presidential Guard (Greek: Προεδρική Φρουρά), an elite ceremonial unit that guards the Greek Tomb of the Unknown Soldier (Greek: Μνημείο του Άγνωστου Στρατιώτη), the Presidential Mansion (Greek: Προεδρικό Μέγαρο) and the gate of Evzones camp in Athens. The Evzones are also known, colloquially, as Tsoliades (Greek: Τσολιάδες; singular: Τσολιάς - Tsolias). Though the Presidential Guard is a predominantly ceremonial unit, all Evzones are volunteers drawn from the Hellenic Army's Infantry, Artillery and Armoured Corps. Prospective Evzones are usually identified at the Army Recruit Training Centres during Basic Training; there is a minimum height requirement of 1.86 m (6' 1.2") to join. The unit is famous around the world for its unique traditional uniform, which has evolved from the clothes worn by the klephts[1] who fought the Ottoman occupation of Greece. The most visible item of this uniform is the fustanella, a kilt-like garment. Their proven valour and peculiar dress turned them into a popular image for the Greek soldier, especially among foreigners. http://en.wikipedia.org/wiki/Evzones

Quote:

From 1453 with the fall of Constantinople until the revolution in 1821 Greece is under the rule of the Ottoman Turks who control the entire middle east, and the Balkans as far as the gates of Vienna. http://www.ahistoryofgreece.com/turkish.htm

That is across the street from Syntagma square http://en.wikipedia.org/wiki/Syntagma_Square

When I was there (October, 2013 ) there were the beginnings of protests/riots. The antiquated uniformed (silly looking) soldiers are an honor guard in front the Greek Tomb of the Unknown Soldier.