A reagent is an item that must be present in a player's inventory in order to cast certain spells, combat abilities, or AA abilities. Actions that require reagents usually are unique in their function, only need to be used rarely, or both. The overwhelming majority of abilities requiring reagents are spells.
Typically, a set amount of the reagent item is consumed with each use of the ability in question. However, some spells requiring reagents simply need for the item to be in the inventory. The druid and ranger spell Flame Lick is one example: the caster must have a Fire Beetle Eye somewhere in his or her inventory in order to use the spell, but the eye is never consumed by being used in this way.
Certain focus effects can reduce the odds that reagents will be consumed. Some AA abilities can reduce (or in some cases completely negate) the chance for reagents to be consumed when using particular spells. For instance, the magician's Elemental Pact AA stops Malachites from being consumed when summoning an elemental pet.
If a spell that normally requires a reagent is being cast as the result of a proc, or as a clicky with no casting time, no reagents will be consumed. Numerous items with procs or clickies of enchanter or wizard rune spells (most of which normally require reagents) take advantage of this fact.