There are at least two types of hallucinations used by the protoss. The first are psionic illusory duplicates of other beings/vehicles, courtesy of psionic powers. This psionic ability to create hallucinations can be used by high templar though the Dark Templar are able to employ a similar technique on their ships. These phantasms are without physical substance.
The second version is technological, used by sentries. These hallucinations are composed of solid light and are three-dimensional, able to mimic protoss warriors, vehicles, and constructs. Each replica, while limited in duration, is able to withstand some degree of punishment.
The high templar selects a unit, creating two duplicates of it. Hallucinations appear with a blue tint to the creating and controlling player, while all other players will see them as duplicates of the original. Hallucinations do not inflict damage when they "attack", may not cast spells, or produce units (important for hallucinated carriers and reavers), and take double damage from all attacks. Hallucinations last for a limited time and automatically disappear when hit by spells (eg. EMP shockwave, Mind Control).
Sentries produce false copies of units to distract opponents. Duplicates have the same number of hit points as the original but take double the damage. The number of hallucinations created depends on the unit: gateway units spawn in twos, probes in fours, and all other units spawn one.