So I guess to expand on Salsa and Het nkik's synopsis, a few things to note:
-The vortex actually devours the entire ocean every 500 years, not just dolphin. You find this out from an ancient blue whale who had the knowledge passed down to him.
-The helix being you meet is called the Asterite. What it exactly is, is never explained, but it seems to act as a god of sort for Earth. when you first meet the Asterite deep in the middle of the ocean, he is weakened and dying because one of his globes is missing. Later, when you time travel at atlantis and meet a younger, more immature asterite, you attack it and steal it's globe, creating a time paradox. The asterite in the present is weakened, because you stole it's globe in the past.
-The Asterite grants Ecco the ability to live without breathing. He no longer has to take breaths of air under water and can survive in space thanks to this. From this point on in the game, you no longer have an air meter.
-Ecco goes back to atlantis and uses the time machine to go back to the very beginning of the game, when he jumped out of the water and missed the vortex spout. He stays under water while this happens this time, and manages to follow the spout through space thanks to the power granted by the asterite.
-Also, while humans are never referenced in-game in either Ecco the Dolphin or Tides of Time, the Sega CD version's manual opens with a small bit of dialog from mankind. It hints that Ecco the Dolphin actually takes place far into the future, when mankind has abandoned Earth. It sounds like they understood about the Vortex queen and were leaving the planet for safety, and is framed around some sort of planetary council arguing the merit of leaving the planet. One side argues that if they leave the planet, then all the remaining life on the planet would be doomed, while the other side argues that mankind should leave behind bits of technology to aid what will become the new dominant species on the planet (given their intelligence) - dolphins. This sort of hints what the glyphs in the game are supposed to be. This bit of backstory isn't in the genesis manual.
Salsa's recount of Ecco: The Tides of Time actually confuses parts of Ecco: Defender of the Future. The recollecting the ocean's consciousness stuff is from defender of the future. Rather, in tides of time, you merely spend a bit of time in each timeline - one thanks to a time traveling dolphin, and one thanks to being kidnapped by vortex spawn. This happens to let ecco know that he must change the future to one or the other by defeating the Vortex Queen, who traveled back to earth.
Ecco: The Tides of Time also ends on a cliffhanger and had hooks for a third game. Midway through the game you were given a useless password - it was supposed to be entered at the beginning of the third game to continue some progress and slight choice changes you made in Tides of Time. Tides of Time ends with ecco chasing the vortex queen to the time machine in atlantis as they do battle. The queen escapes to the past as Salsa said and gets trapped there and evolves into crustaceans over eons, but more interesting is Ecco himself. He gets forever lost in the tides of time and is never seen again. Ecco 3 would have picked up the story and explained what happened to him.