From Bulbapedia, the community-driven Pokémon encyclopedia.
A Legendary trio is a term used to describe a group of three closely-related Legendary Pokémon. Legendary trios can be subdivided into two tiers: normal trios and Special trios. Normal trios, which are always the first legends that appear in any Pokédex order, are allowed into the many Battle Towers and other battle facilities. They are also the only Pokémon with base stat totals of 580, besides the Swords of Justice. Special trios, whose name comes from the fact that all of them are Special Pokémon, are not allowed in the Battle Tower and are found closer to the end of the Pokédex in the generation of their release.
Members of Legendary trios often, but not always, share at least one type, an Ability, and/or their base stat total.
The term fell into official usage from the Shiny Legendary beasts' Wonder Cards.
List of Legendary trios