The Almighty Tallests are the leaders of the Irken race that are chosen for their height.
In the show, they both despise Zim, a young, ambitious Irken whom they sent to the previously thought to be fake planet "Earth", only to realize that Earth was actually real. They often appear in episodes where they reluctantly check up on Zim and his "mission". They first appeared in "The Nightmare Begins."
The Red Tallest is very cunning and calculating, tricking Zim into going to Earth in the first place. The Purple Tallest is rather idiotic and slow.
They both love to eat junk food and like sending young Irkens on missions to other planets. Both are the true main villains in the series.