The Metroidvania style of gameplay focuses on free exploration of one large 2D open world. It is so named as a portmanteau of "Metroid" and "Castlevania" as the style is largely attributed to the Metroid and Castlevania franchises.
The first Metroidvania-style games were released for Japanese computer platforms in 1985: the relatively obscure Sharp X1 game Brain Breaker and the more popular NEC PC-88 game Xanadu: Dragon Slayer II. The following year, this style of gameplay was refined and popularized by the original Metroid, released for the NES in August 1986. The second Castlevania game Vampire Killer, released for the MSX2 in October 1986, used this open-ended style of gameplay, which was further refined by Castlevania II: Simon's Quest for the NES in 1987, before later Castlevania games reverted back to a more linear style of gameplay. A major milestone for the Metroidvania style came with Super Metroid on the SNES. Its refinements to the formula was later borrowed and further proliferated by Castlevania: Symphony of the Night and its portable sequels based on the same format.
The game world in a Metroidvania game is designed in a non-linear fashion, allowing players to explore the world. However, there are usually limitations to a player's exploration, such as out-of-reach areas or areas blocked by an obstacle only destructible by a certain attack. Such limitations are subject to completing certain objectives or finding new tools, and backtracking to and revisiting older areas are hallmarks of this style of game. There are other free exploration designs besides the Metroidvania, and it could be argued that the original Legend of Zelda had an incredibly similar design mindset. The primary difference is the camera view. Most games that allow free exploration use a 3D or overhead (a.k.a. top-down) view. In the case of a Metroidvania game design, the layout is that of a side-scroller. In addition to being a side-scroller, it is the first game type that allowed the player to explore both right and left in addition to climbing upward and falling down.
When the Metroidvania style of play was created, it conflicted with a number of established video game concepts. For example, there were no longer any levels. Since the game was non-linear and allowed free exploration, levels ceased to exist. Instead, the game is broken up into areas, or worlds, that are all seamlessly connected. Each of these areas typically have a unique visual style and/or musical score to give the area definition. Scores were also taken out. This was replaced with speed running. Speed running focuses on the amount of time a game took to complete and how much was done (ex: percent of power-ups collected). This also popularized the 100% run. Players are encouraged to take up this run for unlockables and/or alternate endings. Another form of speed run takes the opposite approach and encourages the player to run through the game while collecting the absolute minimum number of power-ups required to complete the game.
The concepts of a single large world, free exploration, and the obstacle-powerup-backtrack cycle were re-created in polygonal 3D for Metroid Prime and its sequels. Though it may not technically be considered 100% adherent to the style, given its first-person viewpoint and polygonal 3D world, critics noted that this was a very successful transposition of the style's core tenets into a different environment.