As told in "The Gospel Truth", the Titans ruled over the world back when it was still new. They caused mayhem and chaos with their powers. While not mentioned in the song but instead mentioned in the animated series, they were led by Kronos. Then Zeus appeared and locked them in Tartarus after battling them (the animated series says that all the gods of Olympus fought the Titans but "The Gospel Truth" implies that it was just Zeus).
During their imprisonment
Centuries after the Titans were imprisoned, Zeus's son, Hercules, was born. Hades feared that Hercules would screw up his plans to overthrow Zeus. So he went to Fates who tell him the in eighteen years, the planets will align and open the gates to Tartarus and that Hades will free the Titans and use them to take over Olympus as long as Hercules doesn’t fight in the battle.
This prophecy gave birth to Hades' rivalry with Hercules and his many attempts to kill the boy. Hades tried and failed multiple times to destroy Hercules; both during Herc's time at Prometheus Academy and after Herc became a big time hero. In the episode, "The Hostage Crisis", several terrorists representing the Titans held Prometheus Academy hostage until they released Hercules to them.
After zapping the strength out of Hercules, Hades goes to Tartarus and frees the Titans due to the planet aligning. The Titans immediately go on a rampage of destruction chanting "Destroy Zeus", only to find out from Hades that they are heading in the wrong direction. After about facing, Hades sent Cyclops to destroy Hercules.
The Titans launch their attack on Olympus, using Stratos’s vortex to capture most of the gods. Zeus temporarily holds them off with his thunderbolts but when Hephaestus is captured, Zeus is left defenseless. Hydros and Pyros use this to their advantage and trap Zeus in a pile of cooled lava rock.
The Cyclops's battle with Hercules started off to his advantage but Hercules pulled through and defeated the giant. With renewed confidence and strength, Hercules goes to Olympus to save the day. The Titans try to stop him, comically harming Hades in the process but Herc is successful in freeing Zeus and the other gods.
With the Titans caught by surprise, the Gods are able to scare the Titans away. Hercules chases after them, grabbing Stratos and using his vortex to trap the other Titans. Hercules the promptly hurls the Titans into space, banishing them forever.
Hydros is most commonly known as the "Ice Titan" and The "Lurker". As suggested by this title, Hydros is made of solid ice. According to Kingdom Hearts, the ice on his body is too tough to penetrate but his face is very fragile. When he walks, his feet break off and new ones grow in the old ones place. Hydros is one of two Titans featured in Kingdom Hearts and is one of the four Hidden Bosses of the game. He is fought in the Platinum Match and is often considered the fourth hardest boss in the game (losing only to Sephiroth, Phantom, and Kurt Zisa). He is either based on Coeus or Oceanus from Greek Myths.
Pyros is most commonly known as the "Lava Titan" and the "Lord of Flame". As suggested by this title, Pyros is literally a walking volcano. Due him being made of lava, he cannot be harmed by physical attacks. His movement and appearance greatly resemble Jabba the Hutt from Star Wars. Pyros was not featured in Kingdom Hearts for unknown reasons. Pyros did, however, make a cameo in the Kingdom Hearts manga when Hades talks about his plan. He is based off of Prometheus who brought fire to man. He may also have been based on Perses, the Titan God of Destruction.
Stratos is most commonly known as the "Tornado Titan" or the "Wind Titan" and The "Mystic Voice". As suggested by this title, Stratos is one giant tornado. As is the case with Pyros, it cannot be harmed by physical attacks. Stratos appears to be the most powerful of the four Titans as it is able to suck up all of the gods within his mighty vortex. For reasons unknown, Stratos was also left out of Kingdom Hearts but made a cameo in the manga. Stratos does not appear to have been based off of a certain Titan of mythology but it may be based off of Crius or Astraeus the Titan God of the Winds.
Lythos is most commonly known as the "Rock Titan" and the "Mountain King". As suggested by this title, Lythos is made of solid rock. He is the only Titan to have two heads but according to Kingdom Hearts, "can only think with one at a time". Lythos appears to be the most durable Titan as he is hit by Zeus's lightning bolts several times but is never slowed by them. He is one of the two Titans featured in Kingdom Hearts. He is the champion of the Hades Cup and has the most health of any boss. Despite this factor, most players consider him weak. He seems to be based off of Atlas.