Azers are a species of dwarf-like elemental native to the settings of Dungeons & Dragons and Pathfinder. Originating out of the Plane of Fire, they were originally classified as "elemental kin" in Advanced Dungeons & Dragons, as they are denizens of the Elemental Planes that are neither genies nor vanilla-elementals. These elementals were created for AD&D, first appearing in AD&D 1e's Monster Manual II, they then went on appear in Practical Planetology for Spelljammer, then Secrets of the Lamp for Al-Qadim, and finally were reprinted in Monstrous Compendium Annual Volume One from their Al-Qadim statblock. After this somewhat inauspicious start, they went on to star in the Monster Manual for every subsequent edition.
As mentioned above, azers are "dwarf-like". What this means is that an azer resembles a dwarf with metallic skin (copper, bronze or brass, depending on where you look) and with fire for hair. Their bodies emanate extreme heat, allowing them to render metallic weapons they hold burning hot so they can deal extra fire damage, and their skin is unnaturally tough, giving them a pretty good armor class for a race described as preferring to run around in aprons and kilts. Of course, being cretures of burning heat, they really don't like cold very much.
Culturally, azers suffer from the standard problem of elementals throughout most editions of the Great Wheel: very little is actually known about them, save that they live in a rigorously stratified society - somewhere between collectivism and caste-based - under the command of mysterious nobles, ruled over by a King named Amaimon. Like the dwarves they resemble, they are master crafters and produce some of the finest metalwork in all the multiverse; for this reason, efreeti are particularly fond of enslaving azers to serve them.
You may be wondering just why azers look like dwarves? Well, in AD&D, it was just one of the way things were, same with why eladrin looked like elves despite being angels. In 3rd edition, the answer was, essentially, "convergent evolution" - they were fire elementals who just happened to evolve into dwarf-like forms, much like how the elemental planes were full of elementals who just happened to roughly correspond to bears, sharks, etc.
4th edition decided to tweak it: the reason azers in the World Axis look like dwarves is because they were dwarves, or at least their ancestors were. See, in the World Axis, at the dawn of time, dwarves were enslaved en-mass by the giants, who were elemental beings created by the Primordials. Although Moradin ultimately freed them as part of the Dawn War, for some clans, he came too late. Generations of living in places abounding in elemental energy contaminated them, permeating their bodies and souls, changing them. The lucky clans escaped as the Forgeborn, essentially a dwarven analogue to genasi. The unlucky ones completely metamorphosed into elemental beings themselves. Azers, as you can probably figure out due to not having brains made of soap, were slaves to fire giants, and ultimately mutated into fire elementals. They still tend to serve fire giants, efreets and other fiery masters, simply because they have a kinship with them.
Ironically, 5th edition went on to change this drastically: 5e's azers are a species of elemental constructs; golem-like outsiders comprised of a fiery soul inhabiting a dwarf-shaped shell of bronze, which means they literally forge new generations into being.
|The inhabitants of the Planes of Planescape|
|Upper Planes:||Aasimon - Angels - Animal Lords - Archons - Asuras - Eladrin - Guardinals - Lillend|
|Middle Planes:||Formians - Githzerai - Inevitables - Marut - Modrons - Rilmani - Slaadi|
|Lower Planes:|| Alu-Fiends - Baatezu - Bladelings - Cambions - Demodands - Erinyes - Hags |
Hordlings - Imps - Kytons - Marilith - Obyrith - Succubi - Tanar'ri - Yugoloth
|Transitive Planes:||Astral Dreadnought - Githyanki|
|Inner Planes:||Azers - Elementals - Genies - Grues - Mephit - Salamanders - Sylphs|
|Sigil:||Dabus - Cranium Rats|
|High-ups:||Archangels - Archdevils - Archfey - Archomentals - Demon Princes|