From Bulbapedia, the community-driven Pokémon encyclopedia.
First appearing in the Generation I games, a trade machine is the in-game device that players use to trade Pokémon between game cartridges, in addition to the real-world link cable that actually connected information between the games. Players could access these machines at any Pokémon Center in the game by speaking with said Pokémon Center's Cable Club receptionist.
The trade machine is also a device located underneath Pokémon Centers in Pokémon Colosseum and Pokémon XD. It allows the player to trade Pokémon between Orre and the faraway regions of Kanto and Hoenn.
In the anime
Trade machines have been used in multiple episodes of the anime. They are used to trade Pokémon between Trainers, and are usually located in Pokémon Centers. The first was seen aboard the S.S. Anne, in Battle Aboard the St. Anne, but many more have been seen throughout the main series. It was through this method that Jessie obtained her Wobbuffet in Tricks of the Trade. Ash and Dawn also used one to trade Pokémon in Throwing the Track Switch.
Trade evolution was showcased in Evolution Exchange Excitement!, in which Bianca and Professor Juniper traded their Shelmet and Karrablast, respectively, to trigger their respective evolutions.