The Irken History refers to the history of the Irken race.
The First Irkens
The Irken race is presumably unable to reproduce naturally, as they are shown to do so by cloning. It is unknown how they reproduced before they learned the cloning process, but it is possible that the first Irkens reproduced in the same way humans do, and when they found out how to make clones, they forgot how after using cloning for thousands, possibly millions of years.
The Control Brains are the ones who create the Irken babies, known as smeets, and program their personality and all Irken knowledge into their PAK, as seen in the episode "Parent Teacher Night".The Control Brains are extremely powerful; even the Irken leaders, the Almighty Tallest, must obey them, which makes the Almighty Tallest more like figureheads than actual leaders.
This is an Irken occasion on which the Tallest contact all of the Irken Invaders on duty, and check up on how far each has gotten in their missions to conquer their assigned planet. This generally involves the Invaders having to give a presentation of sorts like an essay or video presentation, depicting their current plan to subjugate their planet's inhabitants, or if they're not sapient, wipe them out.
Seeing as the Tallest are interviewing the invaders, one can assume that the holiday started as a result of the conquest of an enemy planet, possibly the first planet conquered by the Irkens in days long past.
Zim's Impact on Irken History
Zim, an Irken Defective, has caused many atrocities in Irken history, many of which are covered in the cancelled episode "The Trial". A few minutes after his birth, he jammed up a chute with another smeet that created a blackout on Irk, lasting for five years, which became known as "Horrible Painful Overload Day." Later, he and Invader Skoodge were involved in an accident with a security robot, which caused another blackout, this one lasting for four years. This event became known as "Horrible Painful Overload Day Part II".
Tallest Miyuki sent Zim to work as a scientist on Vort Research Station 9, where he created an energy absorbing blob that devoured Miyuki. Her successor, Tallest Spork, was devoured by the blob when it returned to get its collar after one day of ruling. The Almighty Tallest Red and Purple took power some time after this.
Zim was also responsible for ruining Tak's life, when he plunged half the Irken military training planet Devastis into darkness by destroying a vending machine after being unable to grab a snack with a gigantic robot. This trapped Tak in her testing room. The Testing continued on the other half of the planet. When Tak escaped from her room, she pleaded with the Control Brain to let her take her test again, but she said she had to wait another seventy years, and was placed on a janitorial squad on planet Dirt.
Zim has also caused plenty of monster rampages, destruction of satellites and even blew up a planet presumably under Irken control by simply scratching his butt. Zim ruined Operation Impending Doom I by rampaging across Irk, believing it to be an enemy planet, almost destroying the Irken civilization. For this, he was sentenced to work on the Irken snacking planet Foodcourtia for all eternity as punishment for ruining Operation Impending Doom I. However, he escaped when he heard about Operation Impending Doom II.
Frylord Sizz-Lorr kidnapped Zim from Skool in "The Frycook What Came from All That Space" to take him back to Foodcourtia so that he wouldn't have to do all the work during The Foodening. However, Zim (as usual) escapes again. Zim worked there as a Janitor or Food Cooker, and has worked there since his punishment.
Incredibly, Zim is apparently proud of the disasters he has caused in his life as seen in "The Trial", and is dumbfounded when others aren't impressed as he is with these "achievements" as revealed in the episode "The Frycook What Came from All That Space."
Operation Impending Doom II
With Zim banished to Foodcourtia, nothing stood in the Irken Empire's way of universal conquest now. Irken Invaders were sent out with their SIR Units to enemy planets to observe the inhabitants, find out its weaknesses, and find out what way would be best to conquer that planet. However Zim came to Conventia, expecting to play part in the new operation for galactic conquest and obviously not understanding that he was exiled from the Empire the Tallest tricked him into a "secret mission" to keep him far away from actual plans for conquest, accidentally discovering the planet Earth where he believed he had been assigned to conquer in the name of the Irken Empire.
Planet Blorch, home of the Slaughtering Rat People, was the first planet conquered in Operation Impending Doom II; Almighty Tallest Red decided to make it into a parking structure planet. Invader Skoodge, the conqueror of Blorch, was launched into the planet by the Tallest, as he was poorly judged for being "short and ugly". Almighty Tallest Purple decided that Invader Grapa's name was now Skoodge as he was taller. He appeared to become happy.
However, it seems that other Invaders are doing well in their mission as well, but it is unknown if they have conquered any of their assigned planets. Invader Flobee was being hailed as leader of the rock people as he was seen sitting on a throne while the rock creatures fans him with large leaves. His SIR Unit was by his side. He was wearing a terrible disguise with rocks strapped to his body. Invader Stink was taking a break, with a burning city in the distance. Invader Skutch is seen laughing on top of a burning structure, presumably conquering the planet. Invader Slacks was still trying to conquer Boodie Nen as seen in "Walk For Your Lives" and was wearing a horrible disguise (Fake nostrils on his face) that still managed to fool the Large Nostril People while Invader Tenn's mission seemed to be failing because of some insane SIR units destroyed her base, exposing her to the Meekrob.
Irken-Planet Jacker Treaty
Main article: Irken-Planet Jacker Treaty
The Irken-Planet Jacker treaty was a treaty signed by the Irkens and the Planet Jackers at an unknown point in Irken History. The treaty restricts the Planet Jackers from throwing planets marked for conquest by the Irken Military into their sun. Zim mentioned this when the Planet Jackers Nik and Oog-Ah try to steal Earth.
Similar with the Planet Jackers, the Irkens signed a treaty with the Inquisitorians at some point in Irken history, presumably in recent times. The treaty outlined the permitted scope and jurisdiction of all Inquisitorian operations. It can be assumed that this treaty allowed Inquisitorians to do research within Irken territory.
The Fall of the Irken Empire
Had the series been completed, there would have been a two part season two finale in which Invader Tenn was discovered by the Meekrob and subsequently captured, endangering Operation Impending Doom II. In response the Tallest would have assembled all the other Invaders on a rescue mission minus Zim who they feared would screw things up.
Zim of course finds out through Skoodge and they leave to "help". Dib would have also found out and travelled to Meekrob most likely using Tak's ship, after much struggle he would've rallied several conquered races against the Irken Empire, which would have been assaulted by the vengeful aliens they once enslaved, reversing the roles of the Invaders and Invaded. Zim and Gaz would have also dethroned the Tallest, taking over and possibly putting an end to the war.
However, given that this episode was never produced nor a script even completed, whether it counts as canon is debatable.