Not to be confused with Alternating.
Double tapping is a tapping style for osu! in which players click circles, slide sliders, and spin spinners by pressing down on both of their set keys on their keyboard (Z and X by default). This style is most often used as a temporary substitute tapping style for extremely fast stacks and streams that are otherwise too difficult for some players. This style is known to be the least accurate.
Double tapping is typically substituted in-place of a player's primary tapping style due to it's easy-to-execute form and increased "speed" (even though the player isn't actually tapping any faster). This increase in speed is achieved by taking advantage of the overlapping hit windows that occur most frequently in stacks and streams. So once one key's input is registered as hitting one circle in a stack, the next circle will also be registered as hit due to their hit windows being so close together that they overlap. But as a result of this, it's almost impossible to control the timing of these hits which can take a toll on the player's accuracy.
Arguments in favour of double tapping typically reference that it is a quick way to allow the player to learn the movements of the beatmap that come after the troubling pattern, while players against double tapping argue that it's a cheap way to get past a difficult section that should be learned.