Centred around the flea market, Monastiraki is a busy square of musicians, beggars, street performers, and tourists. Sometimes you'll hear fireworks going off here, for no particular reason. Sometimes there'll be full-on drum circles.
The flea market surrounding the place is diverse. You'll find all the regular 'ol touristy souvenirs, but also many locally-produced foods. Food is doled out traditionally, here: you go to the cheese shop for cheese, the bakery for bread, etc. The meat market and fish market are also nearby, but those are only for the brave.