After one of the Invaders successfully undermines the defenses of their assigned planet, the ships in the Armada position themselves over a targeted planet and bombard its surface with all of their artillery.
The end result is devastating - all cities on the surface are destroyed, and any structures, flora, or fauna caught in the initial blast zone are thoroughly eradicated and the planet's inhabitants are either enslaved or wiped out.
In "Battle of the Planets", Irken ships could be seen burning a massive Irken insignia into the Blorch's surface with lasers. This may or may not be standard procedure in order to "mark their territory" and let the rest of the universe know that the planet is now under Irken control, afterwards they give the planet itself a sole purpose.
Not all of the motives behind the Organic Sweep have been completely defined (although, according to Invader Skoodge, it's "so that no Irken boot has to come into contact with any unsavory alien filth"), though one theory poses that it's used to reduce the surface of a conquered planet into flat ground, clearing the way for Irkens to begin terraforming (or Irken-forming). However, as this practice has been only seen once, one can only guess as to what occurs after the burning of the Irken symbol.
Another possible theory of what the Organic Sweep does also includes the idea that due to the apparent xenophobic tendencies of the Irken race, as they believe themselves to be superior to any and all other life forms and erasing them from existence may simply be the confirmation they desire, they carry out Organic Sweeps to destroy all remaining opposition to reduce contact with "inferior" species (however, due to the vagueness of the operation and apparent survival of Skoodge after being launch directly into the blast area, it seems more likely that extermination of all life on a planet is not the purpose of the sweep).
Alternately, if it's a complete destruction of all life on the planet, it might be only used in specific scenarios and creatures such as the Slaughtering Rat People were either too dangerous to be kept alive or they were too primitive and not intelligent enough to enslave for manual labor, as was the fate of Smikka Smikka Smoodoo and his people.
The Organic Sweep is carried out after an Irken Invader weakens the planet's defensive capabilities, if there had been any to begin with; likely to eliminate any sort of retaliation against the approaching fleet. According to Skoodge, the Invader responsible for the conquering of the planet has the honor of firing the first cannon.
Zim himself makes such a reference when he plans of "firing the first falling of Earth's organic sweep" when telling the Tallest to prepare the Irken fleet.