Fire is one of the Mage's talent trees that focuses on dealing great sustained damage while providing excellent mana efficiency; Mages who mainly invest into this tree are referred to as fire mages. Fire builds are quickly becoming the default raid build because of talents like Molten Fury which increases a mage's damage vs targets with less than 35% health by as much as 12%. Fire mages excel in mana efficiency when combining talents like Master of Elements and Arcane Concentration (from the arcane tree) essentially giving the mage a chance to gain mana back when casting a Fire or even a Frost spell. Ignite, a staple talent of the Fire tree makes critical hits from fire spells even more dangerous, setting the target ablaze further damaging them for an additional 40% damage when maxed. Pyroblast and Fireball are used to damage the target at range, and Fire Blast, Blast Wave, and Dragon's Breath are all instant-cast spells that can be chained together to finish off the target. In AoE Grinding, fire mages rely on Flamestrike in combination with Blast Wave, Dragon's Breath, and the occasional Frost Nova to lock enemies in place.
In PvP, the Fire Mage philosophy is: "The best defense is a good offense", due to having a very limited number of defensive abilities such as Blazing Speed. However, when played right, a fire mage can ruin someone's day using Combustion to deliver an onslaught of crits as well as disorienting them with a well placed Dragon's Breath.
In PvE, more specifically in raid and groups, this type of mage really shines maintaining higher sustained DPS than a Frost Mage and better mana efficiency than an Arcane Mage.
PvP Tip: Unless you are 3 minute mage build, this is your best chance of a 1v1 kill with a fire mage. First spell should be Polymorph unless target is already in close proximity, in which case spell order should be Frost Nova followed by Polymorph. Once target has been sheeped the progression is such: Pop best damage trinket, Pyroblast, Scorch, Dragon's Breath, Blast Wave, Fireblast. Let it be known that due to PvP trinkets that allow many players to prematurely escape your polymorph, it may be preferable to go with a Fireball rather than Pyroblast in this spell progression. Assuming that your gear is on par for the level enemy player you are trying to waste and your Combustion is not on a cooldown this should provide you with a kill.