The Adept was one of several NPC Classes introduced in Dungeons & Dragons 3rd edition, a direct response to NPCs and PCs now running off of the same system. It takes the place of Wokani from BECMI, sharing many of the same spells and maximum of 6th level. The other NPC Classes of that edition were the Aristocrat, the Commoner, the Expert and the Warrior, plus Eberron's later addition of the Magewright.
The Adept was a divine spellcasting class that mingled elements of cleric and wizard. It could cast divine spells of up to 5th level and prepared them in advance, but it also possessed a familiar. It's very slightly less squishy than a Wizard or Sorcerer and as a divine caster can wear armor (though it isn't proficient in any). Eberron gave the Adept class a major buff by giving them one domain, gaining the spells (including, by RAW, those of 7th, 8th and 9th level, enabling activation of magic items with them and, with effort, even cheesier stuff) and powers of that domain.
Infamously Adept is tier 4 thanks to the ability to handle a handful of encouters really well while struggling at others due to the limited spell list. This is above the other NPC classes, and actually higher tier than the monk, the paladin, and the fighter. Yes, really. This was a spellcaster's edition, son! Unlike other core caster classes however, only four (all from Complete Champion) new Adept spells were added in the entirity of the system's life. Masters of the Wild suggested a variety of spells that should be added to the adept list, however, and Invoke the Cerulean Sign (Lords of Madness) explicitly says it can be mastered by any spellcasting class. It did however, oddly enough, get a prestige class virtually exclusive to it (it requires Lightning Bolt as a divine spell, something only it, Archivist and Shugenja can do and those two need to get survival as a class skill somehow) in the Hexer.
Pathfinder's only change to adept was the system wide skill changes. Pathfinder's adept has slightly more non-core spells, though none of them are great. It also has a single feat, Adept Channel, with requirements that ensure pretty much only Adepts can take.