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A platform game, or platformer, is a genre of video game. Platformer gameplay is about jumping between platforms or over obstacles. The player controls these jumps and must use skill to avoid their character falling off of platforms or missing jumps. This kind of gameplay, even in other genres, is called "platforming". Games where jumping is not controlled by the player, such as The Legend of Zelda: Ocarina of Time, are not thought of as platform games.
Platform games began as 2D in the early 1980s, and 3D platformers became popular in the mid-1990s. The name describes games where jumping on platforms is a large part of the gameplay. However, platforming is not a pure genre, and often there are other types of genres mixed into it. For example, in a game like Metroid, the player controls a character not only to navigate obstacles, but to fight enemies.
As long as the actually jumping remains a main part of the gameplay, the game can still correctly be called a platformer. Because of this, there are many different types of platformers.