The elementalist—often a Twilight’s Hammer cultist—is an arcanist who specializes in several specific elements of his choice (acid, cold, etc.).[1]
In World of Warcraft
An Elementalist is a mage spends most of his talent points in the Fire and Frost trees, often spending no points at all in the Arcane tree. The name refers to the two elemental magic trees, whereas Arcane is seen as the school of pure mana energy. Elementalist specs were somewhat rare before patch 1.11, but new talent synergy and reduced reliance on key Arcane talents opened up the opportunity for more mages to drop the tree all together.
History
Prior to patch 1.11, the Arcane tree had two key talents that were considered must-have by most mages: 
[Improved Arcane Explosion], which reduced the cast time of [Arcane Explosion] from 1.5 seconds to instant, and 
[Evocation], which required 10 points and which was also talent trained. These talents combined were considered to be a requirement for Mages, which meant that they needed to spend 16 points in the Arcane tree. The always popular 
[Improved Counterspell] was available for two more points, for a total of 18 Arcane for many mages. Early elementalists had to sacrifice these three very popular talents, but the benefit was superior defensive talents such as 
[Ice Block] from Frost, and offensive abilities such as 
[Blast Wave] from Fire.
With the mage talent review in patch 1.11, several changes made elementalist builds more popular. Arcane Explosion was made instant cast without the need for talents, Evocation was made available from class trainers, and certain Frost and Fire talents were improved or added to affect more than one school of magic. For instance, 
[Shatter] was improved to increase critical strike chance for all spells, not just Frost. Talents 
[Elemental Precision] and 
[Master of Elements] were added in each tree that affect both Frost and Fire spells. In Patch 2.0, 
[Playing with Fire] was added which affects all spell damage. These changes have reduced the reliance on the Arcane tree and have added synergy between the Frost and Fire trees that didn't exist before.