The thrones of the Greek gods are the seats owned by the Olympians in the Hall of the Gods. The 12 thrones were arranged in an inverted 'U'. A god's power is connected to their thrones, so destroying their throne is one of the ways to defeat a god, and why Kronos wanted to destroy the Hall of the Gods. They were all built by Hephaestus, with the first throne belonging to Zeus.
However, in the movie they are not arranged with the girls on one side and the boys on the other. Also, where Zeus and Hera are meant to sit side by side at the head (similar to arrangement of cabins at camp), Zeus is all by himself, and they are not divided by gender. The thrones do not appear to match the gods' powers however; instead they appear to be made of white marble and celestial bronze.
Percy sat on Poseidon's throne to try and contact his father. When Poseidon arrived, he would have blasted Percy if he hadn't looked and hesitated. In the end, Poseidon forgave Percy for sitting on his throne, since it was an emergency. Percy describes how he felt when he sat on Poseidon's throne; like he was controlling the whole ocean. He realized how powerful his dad was and felt as though Poseidon should be the one in charge, and thought of how it must be with eleven other gods all trying to get their own way.
Please note that not every throne has been described in the series.
Zeus had a simple throne made out of solid platinum with lightning designs on the sides. It is also known as the middle throne inside the Hall of the Gods. While Zeus was praising the heroes that saved Olympus from Kronos, he also pointed out his throne was a little dented.
The throne is made out of ivory and it has a picture of a willow and peacocks on it.
According to Percy, it isn't nearly as grand as Zeus' throne. It has a molded black leather seat which was attached to a swivel pedestal, and with a built-in holster for a fishing pole. Instead of a pole, the holster held a bronze trident, flickering with green light around the tips. Basically, it looked like a chair on a deep-sea boat, that you would sit in it if you want to hunt shark or marlin or sea monsters.
The throne is woven out of apple tree branches, wheat stalks, and dried grass. It has a small yellow seat cushion to sit on
His throne was made of leather and chrome with large human skulls built into the arms. He sat on a cushion of human skin. While Kronos was destroying the god's thrones, he slashed the arm seat of Ares' throne. Ares sits crookedly on his throne.
The throne is silver with golden basket-work on the back and sides. There is a crown of violets above.
The throne is golden with magical inscriptions carved all over it. It represents the sun, healing, and poetry. The back of the throne is shaped like a lyre, and has a python skin to sit on (see Python or Oracle of Delphi). There is a sun disk above with twenty-one rays made out of arrows.
The throne is made out pure silver. It has two date palms on the back, full moons above, she sits on a wolf-skin cushions and probably some skins unknown to Percy that he saw in The Titan's Curse
Hephaestus' Throne looks like a huge mechanical La-Z-Boy type chair covered with bronze and silver gears. When struck into defense mode, it will whir and hum with secret mechanism and can shoot out tendrils of electricity in all directions.
The throne is silver and inlaid with aquamarines, beryl, and other precious stones. The back is shaped like a large seashell and the seat is made from soft swandown (swans are symbols of Aphrodite and she rose from the sea foam created by Ouranos' blood.
The throne is made out of gray rock. It has ram's heads on the arms and sits on a cushion made out of goatskin.
This throne formally belonged to Hestia. It is usually considered to be on the woman's side due to it's former owner, however in The Titan's Curse it seems to be on the men's. And it also appears that in The Last Olympian, Dionysus grew his throne out of grape vines and sits on a leopard skin cushion (his symbol).
Since the end of The Last Olympian, Hades has a throne on Olympus, but has not made an appearance since Olympus. Before that, he sat on a simple stone chair.
The throne has no description.