The Batcave is the secret underground headquarters of Batman (formerly also to Nightwing and Robin, while also sometimes for Batgirl), consisting of a subterranean complex beneath his alter-ego Bruce Wayne's residence, containing all of the numerous sophisticated pieces of equipment utilized in his long anti-crime crusade.
What became the Batcave was first discovered by Bruce Wayne on the day of his parents' funeral. As their caskets were being taken to the Wayne Mausoleum, Bruce ran off into the woods. As he kept on running, he fell down into a well into a cave with bats, which would inspire him with an idea.
As Bruce grew older and developed the idea to rid Gotham City of the criminals and corrupt, he used the series of the caves underneath the Wayne Manor he fell as a child as his base of operations. Along with Alfred Pennyworth, the two of them built up an underground armory and high tech operations area over the years, with a number of levels along with a secret tunnel entrance that leads from underneath the lake on Wayne Manor's grounds. After Wayne Manor was partially destroyed, Bruce and Alfred installed an elevator leading directly to the Batcave from Bruce's new home, the Glasshouse.
The main floor of the Batcave is where Bruce Wayne works. It consists of different computers so Bruce can hack into websites and CCTV cameras to spy on his enemies. There are different staircases leading to different floors of the Batcave: one leading down to a memorial, one leading to the Workshop and one leading to the Gym.
The weapons room is where Bruce Wayne keeps his standard Batsuit, along with his weapons such as Batarangs, Grapple Guns, tracking device firing rifle, smoke bombs, grenades, and other guns. It also contains a memorial case of Jason Todd's Robin Suit.
The Gym is where Bruce Wayne works out regularly, the room consists of many workout equipment such as Tyres, a Power Rack, Punching Bag, Dumbbells, Barbells, a Prowler, Kettlebells, and many other workout equipment, Bruce used this room to train before his battle with Superman.