Pseudo-Legendary is a fan term for a non Legendary Pokémon from a three stage evolution line with a base stat total of exactly 600 and a slow growth rate needing 1,250,000 experience points to reach level 100. One such line has appeared in nearly every generation.
The games never use the term; players invented it because these Pokémon sit at Legendary power without Legendary restrictions. They can be bred, found more than once, and used in facilities that ban true Legendary Pokémon. The list of final forms is Dragonite, Tyranitar, Salamence, Metagross, Garchomp, Hydreigon, Goodra, Kommo-o, Dragapult, and Baxcalibur. Metagross is the exception on typing: it is Steel and Psychic, and Tyranitar is Rock and Dark, while the other eight are Dragon type in their final form.
They are built to be earned late. Their middle stages evolve at unusually high levels, Deino does not become Hydreigon until level 64, the highest evolution level in the series, and Dreepy and Frigibax stay weak for most of a playthrough before paying off. In the story they often appear in the hands of Champions and final bosses: Cynthia's Garchomp, Steven's Metagross, and the Ghetsis Hydreigon are all remembered fights.
Near misses explain the definition's edges. Slaking has 670 total stats but a crippling Ability and Volcarona has 550, so neither qualifies. Hisuian Goodra keeps the line's 600 total as a regional form. If a new three stage line lands on exactly 600 with the slow growth rate, players will call it the next pseudo legendary on sight.
In play"Train that Dreepy properly and your pseudo legendary will carry the late game."