>>33255415The lore is explained in the sets description, which can be found on bulbapedia. I remember learning about it around the time BKT and BKP came out. Here is the BKT set description for example:
>Pokémon BREAK Evolution opens a new path to power that builds on a Pokémon’s existing strengths and creates all-new battling options! These new Pokémon BREAK come from twin worlds, home to Zoroark BREAK, Mega Mewtwo X, and Mega Mewtwo Y. One world of technology, one world of nature, and all the wonders of BREAK Evolution are yours to explore in the Pokémon TCG: XY—BREAKthrough expansion!And he's the BKP one:
>A Rift Torn Between Worlds!The hour grows desperate, and two worlds stand at the brink! The Pokémon TCG: XY—BREAKpoint expansion reveals the growing rift between the twin worlds, first discovered by Shiny Mega Gyarados-EX. As the rift tears through the skies, more Pokémon are drawn into the struggle, including Greninja BREAK, Luxray BREAK, and Mega Scizor-EX! Can they mend the rift and save both worlds from collision chaos?
This lore is depicted in the cards themselves, such as pic related. Chikorita lives in the world of nature and is looking at a Fennekin from the world of a technology through a rift. Plenty of other cards have references to the lore (but not all of them). You can look them up on pkmncards dot com.
As for every set's description, you can find them on their bulbapedia page and this link lists all the tcg expansions to date:
https://bulbapedia.bulbagarden.net/wiki/List_of_Pok%C3%A9mon_Trading_Card_Game_expansions 