The Executor is the personal flagship of Darth Vader, and is the most feared tool of destruction at the Empire's disposal after the Death Star. Vader rules the ship with an iron fist, and it serves as a command vessel for the entire Imperial Fleet.
It's basically a giant Cheese triangle with guns. No-one wants to work on the Executor because theres a chance Darth Vader might just strangle you on the spot. He does that.
The Executor spearheaded the search for the Rebel Alliance's base under the orders of Darth Vader. Vader was so obsessed with finding the rebels that he damn near rammed the ship into a giant asteroid just to drive them out.
The Executor also took part in the final battle of the Galactic Civil War, centered around Endor. During the battle, the ship's shields were taken offline by concentrated fire from Admiral Ackbar's fish catapult and a scuppered A-Wing pilot decided to be very smart and, in his last act, he crashed his damaged fighter into the flagship's bridge. Critically damaged, the ship lost orbit and plummeted towards the Death Star, crashing into the station and causing massive damage to the station.