The Pokédex is a machine that records the data of Pokémon that you have caught evolved or traded created by Professor Oak. In the anime though Ash or May didn't have to catch the Pokémon to get their data they simply have to point the Pokédex at the Pokémon and it shows them data. It exists in all Pokémon games. A Pokédex can display a Pokémon's stats, level, and moves.