Triggered Abilities are abilities that activate when certain conditions are met. For example, see Zulaport Cutthroat. It has "Whenever Zulaport Cutthroat or another creature you control dies, each opponent loses 1 life and you gain 1 life."
This ability activates after a creature dies as long as Zulaport Cutthroat is on the battlefield, and allows you to gain one life and negate your opponent's life in the process when the requirements are met. Usually, Triggered Abilities begin the rules text includes adverbs such as "when", "whenever" or "at".
112.3.c Triggered Abilities have a trigger condition and an effect. They are written as "[Trigger Condition], [effect], and include (and usually begin with) the word "when," "whenever," or "at". Whenever the triggered event occurs, the ability is put on the stack the next time a player would receive priority and stays there until it's countered, it resolves, or otherwise leaves the stack. See rule 603, "Handling Triggered Abilities."