Platformer
Also said as Platform game, Jump and run
You move a character through space by running and jumping across gaps and hazards. It promises mastery of your own body: every death is a jump you can see how to do better.
The loop is run, jump, land, fail, retry, so everything rests on how the jump feels. A platformer with a bad jump has no other game to fall back on.
Say it
“This is a precision platformer, so tune the jump first. I want respawn under a second, 100 ms of coyote time, and every death visibly caused by something on screen.”
Where you’ve seen it
Donkey Kong (1981) made the jump the main verb, and its hero was called Jumpman. Super Mario Bros. (1985) added a scrolling world and a run that carries into the jump, and Celeste (2018) is the modern study of how fair a hard jump can feel.
Not to be confused with metroidvania
A platformer usually moves you forward through separate levels. A metroidvania is one connected world that you go back through as you gain abilities, and the jumping is only part of it.