Powered by the Apocalypse refers to the family of table top role playing games using rules based on Apocalypse World. While there is some pretty extreme variance in how these games work the general outline is fairly consistent. Roll 2d6 and add some stat. On a ten and up you get a full success, on a seven through nine get a partial success, and on a six or less you fail. A few games move the numbers around but the full success, partial success, fail trichotomy is at the core of the Apocalypse World and it's derivatives and I don't think I've ever seen a game under the label without it. Beyond that most of the following will be true: PCs will have classes called playbooks, actions that require the players to roll are called moves, the GM doesn't roll dice, and moves are explicitly listed.
Using the original Apocalypse World as an example, the basic moves that all players have are do something under fire, seize by force, go aggro, seduce or manipulate, read a person, read a sitch, and open your brain. Anything not covered by these moves is implicitly cover by GM fiat. Say you want to read a sitch, roll and add your sharp stat, on ten or more ask three, on a seven to nine ask one: where’s my best escape route / way in / way past, which enemy is most vulnerable to me, which enemy is the biggest threat, what should I be on the lookout for, what’s my enemy’s true position, who’s in control here? Those six questions are what players get in the way of options but it is their choice which one or ones to ask. As a general rule the GM decides when rolls occur but the players pick from among the options. For some moves their partial successes have the player choose a cost associated with their accomplishment like that it's unstable or that their character took damage. Some moves don't provide choices but most offer players one or more outcomes.
Most Powered by the Apocalypse games slot PCs into playbooks. Playbooks are essentially character classes or archetypes with specific starting stats and special moves associated with them. One way that playbooks differ from typical classes is that everything that the class can do is printed on the character sheet for that playbook. Custom sheets for classes is not new but making it the default and having it very explicitly list all of the playbook's special moves with check boxes to mark which your character has and which they have yet to get provides very clear expectations and structure. Like the moves this streamlines and mechanizes play such that the options open to players is incredibly clear.
The last mostly consistent point among Powered by the Apocalypse games is the slightly abstract stats. Masks is a teenage super hero PbtA game with the following stats: danger, freak, superior, savior, and mundane. Each of these represents how comfortable the teenage super hero is in a particular approach to life. Danger lets them directly engage a threat, unleashing their power uses freak, superior lets them provoke an enemy, defending someone or something employs savior, and empathizing uses mundane. Masks' shtick is that these stats aren't static. As the PC is a teenager they find themselves being pulled in one or another direction by the adults around them. This is represented mechanically by raising one stat and lowering another so that the sum of the stats remains constant but the PCs aptitudes are changing. Other games like dungeon world use the original six. The original Apocalypse World uses cool, hot, hard, sharp, and weird. Avatar Legends has creativity, passion, harmony, and focus. The Great American Novel uses instinct, personality, and morality. The general range for stats is -2 too +3 which get added directly to the roll.
Taken all together the entire Powered by the Apocalypse family all act as genre fiction simulators. This should be contrasted with other game systems which are genre fiction world simulators. Other games try to create self consistent settings that let you plan out your characters load out while trying to keep under their encumbered threshold or model how hard it is to throw a knife at a rope from thirty feet away. By comparison PbtA games say, "you are a cowboy, teenage monster, or thirsty sword lesbian and these are the things that cowboys, teenage monsters, or thirsty sword lesbians do. Who cares about verisimilitude? Have fun!" Depending on your preferences this is likely to be either refreshingly direct and comprehensible or seem constricting and trite. Regardless of which side you come down on, the RPG community seems to like it. There are hundreds of games covering an extremely wide range of genres from the super broad to the super specific and it's probably the second largest RPG family after d20 system stuff. If you want something both lite and crunchy Powered by the Apocalypse is probably your best bet.
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