Originally, every citizen of Athens belonged to one of four tribes. This, and the fact that the word Athens is plural even in the original Greek, might mean that Athens was founded by four local villages which came together to form a city, back in pre-historic times. No one really knows, but it's a guess.
The tribes had a real social function even into Classical times: almost all big events were managed on a per tribe basis. Because the tribes were groupings of families, essentially clans, they also tended to become a problem in political questions. Alliances would form or dissolve based on who was in what tribe.
After the last tyrant of Athens fell in 510BC, fifty years before my first story, a man called Cleisthenes rose to great influence. Cleisthenes is sometimes called the Father of Democracy because he instituted a large number of reforms all designed to drive Athens in that direction. He didn't quite get there -- that was left to Ephialtes in the next generation -- but he was fundamental in creating all the necessary social structures.
One of the things Cleisthenes did was expand the four tribes into ten. The population had grown and there were so many people that four tribes weren't enough. Cleisthenes also wanted to allocate men to tribes in a more or less random way, so that the power of the larger families was broken.
By the time of Nicolaos and Diotima, the tribes had become pure and very handy administrative groups.
The ten new tribes were named after famous men of the past. They became known collectively as the Eponymous Heroes and a statue to them was set up in the Agora. Here's an excerpt from my first book. Nicolaos is wandering about the Agora.
I wished them luck and went on my way, coming to the statues of the Ten Heroes, each of whom lends his name to one of the ten tribes. All the people of Attica – the large region of mainland Greece which Athens controls – belong to one or the other of these tribes, and Government jobs are shared equally among the men of each tribe so that no group can have too much influence.
The Ten Heroes are spread out in a line, each hero in such a noble pose that I’m sure his own mother wouldn’t have recognized him. Eight of the Ten were famous Kings of old: Ægeus, Erechtheus, Pandion, Oeneus, Leos, Acamas, Cecrops, and Hippothoon; then there was Ajax, who fought at Troy, and finally Antiochus, the son of Heracles, the tribe to which my own family belonged.
These then were the famous heroes of old, their statues in the Agora, and not for the first time I wondered why Theseus, surely the greatest hero Athens ever produced, was not among them. Theseus after all sent himself as a sacrificial tribute to Crete, slew the Minotaur, and returned to Athens having delivered the city from subjugation at the hands of King Minos. You can’t get more heroic than that.
As I always did when I came this way, I walked around to the rear of Antiochus, to check once more on my greatest triumph as a young boy in Athens. There, scratched deep into the hero’s ass, just below the cloak line, was a large N. It’s very hard to cut graffiti into marble, the other boys had had to make do with ink that had soon washed off; sometimes being the son of a sculptor has its advantages.
The monument serves as the notice board of Athens; anything of importance, any official proclamation, is announced by writing it on the plinth. Someone had splashed whitewash across the plinth, obliterating everything that had been there before, replacing all those words with a single message in large letters: Ephialtes is murdered.
Attica was divided into three arbitrary provinces. Each province was in turn divided into tenths, one for each tribe. Thus a third of each tribe's territory lay in each province, from which they became known as trittyes, which means thirds. Three provinces times ten tribes meant thirty trittyes. Each tritty was in turn broken up into smaller areas called demes. Athens itself was broken up into many small demes shared equally among the ten tribes. In the countryside where populations were lower, demes were larger in area.
Thus a deme was in a real sense like a modern suburb. If you knew someone's deme, which you would because people included their deme when they introduced themselves, then you could turn up at the deme and ask anyone where to find your friend's house.
But in addition everyone in a deme belonged to the same tribe. The affiliation mattered a lot. The archons who ran the city for a year were selected from each tribe in fixed turns. So every tribe got to control Attica and Athens for one year out of ten.
The way you got elected was this: Ten candidates were selected for each archonship, by random lot from amongst the entire membership of the tribe whose turn it was to rule, and then everyone got to vote from amongst the ten. The randomness meant that some years there was nothing on offer but ten losers. If it happened, it happened, and people just had to wear it.
Similarly the council (Boule) which arranged the agenda for the city's parliament (Ecclesia) consisted of 500 men: 50 from each tribe, rotated annually. Each deme had to supply a certain number of their tribe's 50.
As you can see the whole system was extensively designed to prevent anyone from getting too much power. Every deme had to carry its share of responsibility, and since every government job rotated every year, it meant as long as you were not actually a drooling idiot, you were guaranteed to get a turn as an office holder at some point in your life.