Archetype
Archetypes are a term cum game mechanic introduced to the /tg/ lexicon with the invention of the Pathfinder Roleplaying Game. They are essentially Paizo taking the concept of the Variant Class, which they had worked on fairly extensively in the pages of Dragon Magazine, and making it a core mechanic... more or less. Although archetypes were not present in the Core Rulebook - unless one counts Cleric Domains, Sorcerer Bloodlines and Specialist Wizards - they were very quickly introduced in the subsequent PC-focused books and became a mainstay of the game.
Conceptually, archetypes are simple; you pick a base class, like the fighter, rogue or wizard, and then you can choose to take an archetype, which will alter some of your class features and, if you have a "modular" class like the barbarian, oracle or alchemist, may recommend that you take certain optional class powers - the Mounted Fury archetype for the barbarian really works better if you pick the rage powers that buff your mount when you rage.
One of the oddities of the system is that it has completely swallowed the Specialist Wizard mechanic of old, but it exists largely independently of the various "caster subclasses" for the other spellcaster classes, such as cleric domains, sorcerer bloodlines, and oracle mysteries.
The "subclass" system of Dungeons & Dragons 5th Edition was probably inspired when Wizards of the Coast saw the archetypes of PF1e, realized how popular they were, and decided to make them not just a core mechanic but a mandatory class choice.
Starfinder acted as a sort of interquel between the two editions of Pathfinder, though it felt more like Prestige Classes than merely changing a base class. These archetypes were applied equally to all classes, meaning that they always activated at certain levels, replacing specific class features or delaying when they're gotten. These archetypes also tended to either apply membership to some organization or channel some sort of innate power. Alongside these are also the "Alternate Class Features", which was salvaged from the old 3.X bin, which allowed you to swap out one class feature for another of equivalent value.
Pathfinder Second Edition also had archetypes, but these were made more in the line of feat trees like in D&D 4e with a mix of Prestige Classes for the various archetypes that aren't based on base classes.