The Trident is a sacred relic that gives its wielder the ability to control the sea, or Atlantica. It is more of a spellcasting weapon than a melee weapon. King Triton is the current wielder of the Trident.
Powers
Its main power is shooting a large blast of yellow energy at a certain target. Other powers it has, examples have shown, are manipulating water and changing the present state of a being. In Kingdom Hearts II, King Triton uses it to write his name on a contract. When wielding the Trident, Ursula uses some thunder and blizzard-type attacks during the second boss battle against her, but it is not certain that all these attacks were the power of the trident. The Trident can also grow and shrink with its user.
Story
Kingdom Hearts
King Triton uses the Trident to destroy when Screwdivers attempt to invade the castle, and later destroys the Crystal Trident, which is actually the key to revealing Atlantica's Keyhole. Ursula eventually steals King Triton's Trident, and grows to a gigantic size. Sora and co. defeat her, and then they use the Trident as a replacement for the Crystal Trident to seal the Keyhole.
There are also markers along the walls in Atlantica that points to the Palace that are in the shape of the Trident.
Kingdom Hearts Chain of Memories
When Sora, Donald, and Goofy sees Ariel swimming past them carrying the Trident, she tells them to not tell anyone that they saw her. Sora and co. enter the palace and find that the Trident was stolen and that Ariel has gone missing.
Later, Sora and co. find out that Ariel stole the Trident but only to help Flounder who had been lost in the surface world. Ariel was going to give it to Ursula she said that giving her the Trident was the only way to save Flounder. They all traveled to Ursula's Lair, finding that she kidnapped Flounder as a way to get the Trident, which Ariel gives over to save Flounder.
In the end, Ariel reclaims the Trident and Sora suggests that she should say she found the Trident and got it back all by herself. However, she says she can't do that because it was her mistake which she made to help her friend. She wants to tell the truth when she returns the Trident.
Kingdom Hearts II
The Trident only appears in scenes with Triton and the song-battle against Ursula, where she uses it as a weapon once again. During the battle, Ursula uses it to deflect Sora's attacks and to attack Sora, Ariel and the others. At the end of the song, Sora successfully knocks the Trident out of Ursula's hands, and it lands in Prince Eric's boat. Eric then uses it as a javelin to defeat Ursula once again. The trident is last seen being used by King Triton to light the palace chandelier during the "A New Day is Dawning" musical.
Etymology
A trident is the royal scepter of Poseidon and Triton in Greek mythology, both who were gods of the ocean and water.