The Greeks took games of all kinds very seriously, but especially physical athletic competition. The Greeks believed that their gods especially loved to see strong, fit, graceful human bodies, especially boys’ and men’s bodies.
So one way to get on the good side of the gods was to exercise, to eat right, to oil your skin, to create a beautiful body that the gods would love. Because of the Greek tendency to turn everything into an agon, a competition, this also meant that there were a lot of athletic competitions in Greece. The most famous of these is the Olympic Games, but there were other games held in other places as well, like the Isthmian Games at Corinth.
Young men (from richer families who didn’t have to work) in most Greek cities spent a lot of their time training for these competitions, and the best of them were chosen to compete against the best young men from other cities.
Then they would all meet, at the Olympic Games or the Isthmian Games or another festival, and compete for prizes and for the favor of the gods. Of course these games also served as good training for the army, because all these men would be soldiers as well.
The events were the same kind as in the Olympics today: running, jumping, throwing a javelin, and throwing a discus. There were also chariot races and horse races. Only men could compete in the Olympics, but by the time of Plato (and maybe earlier) there were other games where women competed.
Greek boys also played games that weren’t part of the Olympic games, like field hockey. Greek boys usually played games without their clothes on. Greek girls also played games: they juggled and played catch and ran foot-races (but the girls wore short tunics).
The Athenian girl in this picture is juggling three balls. In southern Greece, in Sparta, girls had organized races and competitions. Greeks also played less active games like dice and marbles, and knucklebones, and checkers.
In this Hellenistic scene, two girls are playing knucklebones, which was a game like jacks. (To Greek people, teenage girls playing knucklebones was a metaphor for the hit-or-miss gamble of marriage they were facing).
Even in these games, though, the competition was very important, and there was a feeling that losing at games meant that the gods didn’t like you.