For the Greeks, the word 'tragedy' was used much as we use the word 'play' - but it does not carry the same implications of our modern word 'tragedy'.
In Athens, the performance of tragedies took place as part of festivals - the most famous being the City Dionysia, a festival which worshipped the god Dionysos. Dionysos is the god of wine, of revelry, of theatre, of frenzy and of ambiguity - a reading of Euripides' Bacchae goes much of the way to explain some of the logic behind his association with the Greek theatre.
The price of a ticket to the festival was distributed by the deme (the local town council) to each citizen whose record was good, and the audience sat in the open-air theatre below the Akropolis, divided into the same ten wedge-shaped sections that they sat in for public meetings. It is extremely clear, therefore, that, in the words of Froma Zeitlin "theater attendance was thus closely linked to citizenship". The Athenian festivals, as well as celebrating Dionysos, were designed to celebrate Athenian democracy and the power of the polis.
The festivals sometimes lasted several days, and involved sacrifices, choral singing, the performances of comedies and religious rites as well as the tragedy competition; and one of the key things to understand about the importance of agon in Greek drama is that these tragedies were written to compete against other tragedies. Budding playwrights submitted three tragedies together (though not always – and, in most instances, rarely – thematically linked together) and a satyr play, and three playwrights were chosen to have their trilogies and satyr play performed in a competition. Ten judges, chosen by lots, would then vote for, respectively, the first, second and third prizes.
The Greek theatre itself was famously built with a fan-shaped auditorium, in what is now called an ‘amphitheatre’ layout. Modern examples of this layout include the Royal National Theater’s Olivier auditorium, and a Greek theatre of this kind survives at Epidaurous (pictured). The stage was likely circular, and the back wall of the stage was probably a permanent stone building, the ‘skene’, in which costumes and props could be stored, and which served variously as the internal locations the play might require (houses, tents, etc.). The performances themselves would have included little or no props, and probably very minimal costumes. The actors probably doubled several roles between them (Sophocles famously used three actors for his plays) and differentiated between them by switching masks.