Dance was an important art form in ancient Greece. Although there were professional dancers, everybody loved to dance. Some dances called for men to dance together. Others were designed for women to dance together. But men and women never danced together, although they might dance in two circles - the woman dancing in a circle inside and the men forming a circle around them on the outside. Dance was accompanied with music.
These dances had set patterns. There were over 200 dances with set patterns for various purposes. The Greeks had war dances and funny dances and funeral dances and wedding dancing and a dance for celebrations, like the birth of a new child.
Many dances were danced to honor a specific god. Apollo was the Greek god of music. One of his nicknames was "The Dancer". Scholars call some of the ancient Greek religious dances Apollonian dances. These dances were always accompanied with musical instruments, especially the lyre. Some of the most famous dances were in honor of the Greek god of wine, Dionysus.
Some dances were danced as part of military training. In ancient Sparta, it was actually the law that parents had to get their kids dancing at age 5 as part of their needed exercise. These dances were led by men and were quite energetic.
Lots of noise went with dancing in ancient Greece. There were bells and tambourines and castanets for rhythm (and noise) along with lyres and flutes for melody.
How to Greek Dance: Hasapiko (youtube, Children's Museum of Indianapolis)
The Dance Teacher, story for kids