Isekai
Isekai is a genre in which a character is transported, reborn or summoned into another world, usually a fantasy world with game-like rules, and has to make a life there.
Where the word comes from
Japanese 異世界, "different world".
In depth
In an isekai story the protagonist leaves ordinary life — often by dying, sometimes by being summoned or trapped in a game — and wakes in another world. That world is usually a sword-and-sorcery setting, frequently with levels, skills and status screens borrowed from role-playing games.
Roots and boom
Portal fantasies are old, and manga and anime had earlier other-world stories such as Fushigi Yūgi and The Vision of Escaflowne in the 1990s. The modern boom came from web novels: amateur writers posting serial fiction on sites like Shōsetsuka ni Narō, then picked up as light novels, manga and anime from the 2010s.
Common types
Reincarnation (the hero is reborn as a baby, a monster or a villainess), summoning (a whole class of students is called to save a kingdom), trapped-in-a-game, and the reverse isekai, in which someone from a fantasy world arrives in ours. That Time I Got Reincarnated as a Slime, Re:Zero and Mushoku Tensei are among the best known.
Manga or light novel
Most isekai manga adapt a light novel, which is usually further ahead in the story.
Where it appears
That Time I Got Reincarnated as a Slime. reincarnation isekai, light novel and manga
Re:Zero − Starting Life in Another World by Tappei Nagatsuki. isekai with a time-loop twist
Mushoku Tensei: Jobless Reincarnation by Rifujin na Magonote. influential reincarnation series
What it means today
Isekai titles are famously long and descriptive. The title often tells you the whole premise, which makes them easy to choose by mood.