Mote of Fire

A Mote of Fire is a small piece of pure fire. It can be found while mining or killing fire elementals, and is used both in alchemy and engineering, as well as for combining into.

Alchemy

 * Elixir of Major Firepower

Engineering

 * Elemental Blasting Powder

No trade skill

 * Primal Fire

As a quest objective
4x Motes of Fire along with some other items should be turned in for the Shattered Halls Key quests:
 * Dumphry's Request (Alliance)
 * Rohok's Request (Horde)

Farming
Since Patch 2.1.0, acquiring Motes of Fire has become much harder, due to changes to some of the most common farming locations. Previously, the two forge camps in Blade's Edge had high drop rates and well placed mobs, but this has since been removed. Now, Motes of Fire are among the highest demanded items in the game, making prices high and farming difficult due to competition.

If you're intending on making a lot of money from farming motes, buying green fire resist gear can be a worthwhile investment. Getting your fire resist up to a good number is very helpful, as the Fire Elementals that drop Motes of Fire only do fire damage, leaving you virtually impervious. However, this can mean you're less likely to be able to kill anything else as quickly, and almost all the locations listed here have other mobs (and other players) in the area.

Miners can acquire a steady supply from their regular mining activities, but for those of other professions, the only way to farm these is to kill lots of elementals. The drop rate is decent.

Fire elementals can be found in the following locations:
 * Skald, Blade's Edge Mountains, off Searing Elementals: The lowest level fire elementals are among the most plentiful. This area is packed with the fire elementals, money-dropping imps, and meat that's cooked into +spell dmg food from the basilisks. The large number of mobs present means that multiple people can farm here, and also that players who arn't level 70 yet can also get some motes outside of the Auction House. However, it does get rather crowded, and the drop rate is among the lowest. Come here if other places are overcrowded, or if you're too low of level to go elsewhere.
 * The Fel Pits, Shadowmoon Valley, off Enraged Fire Spirits: There are plenty of these mobs spread throughout this large area, but the environment is anything but friendly. You'll be dodging regular demon dog and earth elemental patrols, all while trying to stay out of the plentiful lava in the area. In addition, the drop rate is about the same as in Skald, making this place generally inferior.
 * Forge Camp: Terror, Blade's Edge Mountains, off Vile Fire-Souls: In general, this location is quite difficult to farm. Huge Flak cannons shoot anyone on a flying mount out of the sky (or even the ground if you don't get off your mount), and the mobs you're looking for are spread out, patrol, and surrounded by high level demon mobs. The influx of players doing Ogri'la quests means the area is crowded, which is both a blessing and a curse, as they kill the patrolling mobs, but also the Vile Fire-Souls. If other areas are far too crowded or you happen to be in the area, you can try farming a Primal or two here. But for extended grinding, this area sucks.
 * Elemental Plateau, Nagrand, off Raging Fire-Souls: The veritable mecca of mote farming, Elemental Plateau is almost always covered in farmers. Competition for spawns is fierce, making for very ineffiecent work. However, if you can catch it on off hours, the plateau has a large number of spawns, a high drop rate, and every elemental you could hope for. But don't expect much when there's a raging battle between factions running. It is also good to farm here as Oshu'gun Crystal Powder Sample's also drop here.
 * Throne of Kil'jaeden, Hellfire Peninsula, off Incandescent Fel Sparks: Added in Patch 2.4.0. One of the best areas to farm them due to a fast respawn rate and good drop rates. However, the influx of players doing daily quests for the Shattered Sun Offensive means the area is crowded at various times. But be careful, because sometimes they are near Doom Lord Kazzak.