The Old Ones were a group of extra-dimensional entities.
Mightiest among the Old Ones was Icthultu. Due to their appearance and power, they were often regarded as deities whenever they crossed dimensions. So too for the Thanagarians. The Old Ones fed on the worship and sacrifice, but eventually, the Thanagarians rejected them and moved on.
The Old Ones were indirectly responsible for the sinking of Atlantis. They did not get worship from the Atlanteans, thus battle ensued. The Atlanteans were losing ground, until their king, Poseidon, gathered all the ambient mystical power on the planet to forge a magical trident. The Old Ones were cast back to their own dimension. The loss of the magic around Atlantis doomed it: it sank beneath the waves.