If the Greeks are so tied to their poleis, what could it possibly mean to be Greek? How one defines oneself as Greek in Ancient Greece is different from how we define ourselves as Americans.
There are several characteristics or traits that define you ask Ancient Greek. A trait is something you can see or use to put an item or a person into a specific category. That means we are trying to define the specific things we can see that would put a person into the category of being a Greek.
First off is the language you spoke. To be Greek, you have to speak Greek. There are several dialects of Greek. What dialect you speak does not make any difference.
A dialect is just a slightly different way of speaking a language. People in the northern United States speak one dialect of English. People in the southern United States speak another dialect of English. We each sound funny to the other, but we can each understand the other. The same is true with the Ancient Greeks. The Dorians spoke one dialect. The survivors of the Mycenaean Greeks spoke another dialect. But they could both understand each other.
A common Greek language means the Greeks thought in the same way. The Greeks thought of the world is divided into those who spoke Greek and those who did not speak Greek. The people who did not speak Greek sounded like they were saying baah, baah, baah. So the Greeks called everyone who did not speak Greek barbarians. This way of thinking created an us easy way of thinking.
The Greeks also shared a common religion. They believed in the same gods and goddesses. They believe that each of god at each goddess had powers over the same things in nature regardless of what is their polis. They follow the same rituals for worshiping these gods and goddesses. They even shared the same shrines for specific gods. For instance, the god Apollo's shrine is at Delphi. Those who wish to especially honor Apollo, regardless of where they live, will make their way to Delphi. All Greeks wil also go to Delphi to have their fortunes told.
Athletic games become an important factor holding the Greeks together. Most athletic games develop out of Greek religion. The most important of these athletic games is the Olympics. The Olympic Games are developed in honor of Zeus , the king of the gods. They are held near Mount Olympus, the location of Zeus' palace, and the center of the activity of all the gods. During the period of the Olympic Games, there can be no warfare among the Greeks. There has to be peace. There has to be piece for the athletes to travel to Olympus. There has to be peace during the games. There has to be piece for the athletes to travel back to their homes.
The idea of peace during athletic games is what we call a custom. It is a rule that a specific group of people follow. The Greeks developed a number of customs they shared in common. In addition to peace during athletic games, there is the custom of caring for a guest. If you have a guest, you are responsible for everything. You are responsible for his food. You were responsible for his clothing. You are responsible for his personal safety. That was a custom among the Greeks.
There are quite a number of customs that the Greeks shared. Sharing these customs and living by them,was part of what it means to be Greek.
A common language, a common religion, and a common set of customs are what determine whether you were Greek or a barbarian!