The Pokédex is the in game encyclopedia that records every Pokémon species the player has seen and caught, giving each a number, classification, height, weight, and a short descriptive entry. Completing the Pokédex, catching every species in a regional or national list, is a standing long term goal of the games.
Professor Oak hands you the Pokédex in Generation I as a request to complete his research, and every game since has kept the structure: seen entries show a silhouette and basic data, caught entries unlock the full text. The entries are canon written by the games themselves, and they are famously darker than the series' image, describing Pokémon eating each other, haunting people, and dragging prey underwater, all in a device handed to a child.
The scope kept growing. Regional Pokédexes cover one game's roster, the National Pokédex covers everything, and by Generation VII the main games dropped the National Pokédex in game, moving full completion tracking to Pokémon HOME. Rewards scaled with the task: diplomas for completion since the early games, the Oval Charm for completing a regional dex in Generation V, and the Shiny Charm for National completion in Pokémon Black 2 and White 2, which permanently changed how players hunted.
Pokémon Legends: Arceus rebuilt the device as a research survey, where completing entries takes repeated catches, battles, and observations rather than one catch. A living dex, keeping one of every species in storage, is the completionist endgame either way. When a player says a Pokémon's dex number, they mean its National Pokédex position, with Bulbasaur at 1.
In play"I finished the regional Pokédex, but the national one is a whole other project."