Generally speaking, "Wrath effect" is Magic slang for the removal of most, if not all, creatures in play by any spell or ability, as the effect of an instant or sorcery spell, an activated ability, or a triggered ability, or, loosely, any card that can produce a Wrath effect. The effect is named after the card Wrath of God, the first Magic card to feature a mass-creature-removal effect. The precise board impact of a Wrath-effect card is dependent on the current game state, specifically the board condition; but, as a general rule, Wrath effects are extremely powerful and a form of card advantage.
As a slang term, no definitive definition of a Wrath effect exists; but, it is commonly understood that cards such as Wildfire and Destructive Force and cards that do damage to all, or a subset of all, creatures such as Earthquake, Hurricane, and Pyroclasm, regardless of the amount of damage dealt, are not Wrath effects per se due to the additional consideration of creatures' toughnesses and state-based effects; instead, such cards have Wrath-like effects. Other than this, there are essentially no restrictions as to the means by which Wrath effects remove creatures from play, and Wrath effects have included destruction of the creatures, destruction of the creatures without regeneration, removal from the game, and returning to their owners' hands. Strictly speaking, in consideration of the effect of the original Wrath of God, a Wrath effect is any effect that destroys all, or most, creatures, with or without allowing for regeneration.
Colors such as white and blue have variations upon the Wrath effect. One such is non-destructive removal from play, by exiling or moving creature cards to another zone, such as the hand or the library. Black, interestingly and exclusively, has a variation upon the Wrath effect whereby it gives all, or a subset of all, creatures -m/-n (where m and n are constants or variables that are defined by the card). This too takes into consideration creatures' toughness and state-based effects and is thus a Wrath-like effect.