Team Rocket (ロケット団 Rocket Gang) is a Criminal Organization, with their base in the Kanto Region, and branches in the Johto Region, and Sevii Islands. They are headed by Giovanni, who also doubles as the Viridian City Gym Leader.
Team Rocket's main goal is obtaining powerful and rare Pokémon to further their criminal syndicate in hopes of someday taking over the world. They obtain these Pokémon by regular capture, or more often, theft. In addition to this they also preform inhumane experiments on Pokémon to further their power.
Team Rocket mainly refers to the idiot couple from the anime and their Meowth/whatever fourth thing is following them at the time, mostly Wobbuffet. They are horrible at their job, being beaten up by a stupid kid and his stupid friends with his stupid Pikachu on a daily basis. They suck even more as they get further and further away from Kanto.
They have giant robots, and a hot air balloon, and tanks, and all sorts of beastly stuff. But no, these incompetent cronies suck so bad, they have to be dominated by freaking Ash Ketchum. Ash. Freaking. Ketchum. The kid who gave a Gym Leader his Charizard and never want back for it. Sure Ash, that'll make it like you more.
They also are always starving. Always. If you guys are criminals, why can't you go steal stuff to eat. I know why. because you suck at stealing things.
In Anime Edit
Team Rocket, in the anime, have a Base of Operations in Kanto and are headed by Giovanni. Their headquarters were once located in between Pallet Town and Viridian City but has since been destroyed. It is now in an unknown location inside of a large canyon. Team Rocket has also been shown to have branches in the Johto Region and other areas in Kato.