The Iconians are considered the ultimate Bigger Bads (the Primary Main Antagonists) of Star Trek Online and are based on a species of the same name from the mainstream Star Trek lore - it is worth noting however Iconians are only antagonistic in the Star Trek Online universe, in the mainstream Star Trek lore the Iconians were considered extinct long before the Federation existed and thus did not become antagonists.
The Iconians were a galaxy super-power 200,000 years ago but were believed to have become extinct after an orbital bombardment of their world, Iconia - which is situated in what is now the Romulan Neutral Zone.
Although the Iconians rarely expose themselves they did not, despite popular belief, go extinct and instead waged a hidden war against most other species in the Alpha and Beta Quadrants, using the Undine and many others as pawns in a grand scheme of manipulation and conquest.
Almost every major conflict in Star Trek Online is believed to have either been created by the Iconians or as a result of their manipulation - for example the devastating war between the Federation and the Klingons was a result of the Undine inflitration of the Gorn homeworld and the fallout between Starfleet and the Klingon Empire over the Klingons purging of the Gorn homeworld via mass public execution.
The Iconians also helped in the destruction of Romulus and Remus, which devastated the Romulan people and made them an even more dangerous opponent than before.
Ultimately the Iconians goal seems to be to destabilize all major species in the galaxy and so far they have shown themselves to be frighteningly capable of doing so - this is not a surprise as it is stated that the Iconians were designed by the creators of Star Trek Online to be "the ultimate villain".
An Iconian is seen for the first time in 2410 during the STO mission 'Surface Tension'. They are attempting to prevent peace between the Federation and Klingon Empire. In another mission callled 'Uneasy Allies,' they would later on to have been discovered to be based in a Dyson's sphere in the Andromeda Galaxy and had the Romulan Tal Shiar working for them with false promises to bring back Romulus via time travel, but Sela revealed that their minds couldn't handle time travel unlike most beings in the universe.
Somehow they brought the Dyson's sphere they were using as a base to the Alpha Quadrant of the Milky Way Galaxy, which would begin the Iconian Invasion.