An internal cooldown (ICD) is a period after an effect or power triggers in which the game prevents it from triggering again. Internal cooldowns apply to a number of unique powers of items, as well as a few passive skills, each of which has its own internal cooldown period. They are intended to keep the game balanced by preventing an effect from triggering extremely rapidly due to factors like Attack Speed, hitting multiple enemies at a time, or interactions with other powers that might amplify the conditions that cause the effect.
Internal cooldowns are not affected by Cooldown Reduction or other interactions with normal active skill cooldowns.
In Diablo III, a few internal cooldowns are stated in the description of the relevant effect, most notably the "cheat death" passive skills and Follower skills, which cannot save the player more than once every 1-2 minutes (although two different effects could save them in a short period). However, many internal cooldowns are "hidden", although they can be observed by repeatedly and rapidly taking the action that would cause the effect and noting its frequency.
A related game mechanic is a Proc Coefficient: Instead of putting a direct limit on how soon an effect can re-trigger, Proc Coefficients attempt to keep the long term impact of an effect uniform by reducing the chance of triggering when using skills that otherwise might trigger it more than intended.