A StatStick typically refers to a weapon that is not used in attacks but is equipped for its stats. It can also mean an off-hand item (other than a tank's shield) or a relic, since these occupy the same slots as weapons. The term arose because traditionally only staffs, wands, maces and rod-shaped off-hand items fell into this category. However, the scope has broadened with the introduction of caster swords and shields, relics, and off-hand books.
Stat sticks include the melee weapon for a hunter, the ranged weapon for a warrior or rogue, and both for a caster. However, warrior tanks used to sometimes pull using a ranged shot, and casters may use wands at low levels to conserve mana or make use of idle healing time.
BlizzCon 2011 revealed the intention to remove the ranged slot upon the release of Mists of Pandaria. Relics, a concept the designers admitted disliking, were removed. Hunters lost the need to have a melee weapon equipped (though they stil can) and had their ranged weapons equippable in their main hand slot. This left casters with one fewer statstick and eliminated them altogether for non-casters.