Action-adventure or action-platformer sub-genre with a lot of backtracking, a superficial sense of exploration to find locations to which you later gain access to via new abilities, tools, or such.
The first video game about Metroidvania was released in 1984.
* Fairly open environments, with ability to go off exploring in directions, though usually shortly impeded by an obstacle that you need some item or ability to progress through. Gives some focus to exploring and thus actually finding where you need to go.
* Presence of said items and abilities that somehow improve your mobility or allow you to open, disable, or destroy certain obstacles. Opening up previously blocked off areas. This includes just plain keys as the other abilities or items can work the same way as a regular key.
* Lots of backtracking because of #2, and gives off a sense of non-linearity because of #1 even when it isn't actually non-linear (it is not necessary player has choice in the order of area unlocking things).
* Usually only one overall level/map that spans an an excessively large region. Though can easily be spread to multiple maps (e.g. multiple worlds). Usually interconnected even in the latter case.
* Character power dictated by the equipment they have. This is least important feature, and the equipment could easily be provided as abilities instead.