Elliot et al. (2008) define a hallucination as:
A sensory experience which occurs in the absence of corresponding external stimulation of the relevant sensory organ, has sufficient sense of reality resemble a veridical perception (i.e. the perception seems to be "real"), over which the subject does not feel direct and voluntary control, and which occurs in the awake state.
They define illusions as:
These are false perceptions of a real external stimulus, for example a change in shape, size, color or texture. In some cases, where the external stimulus is minimal, the differentiation nosologically (nosology: the classification of diseases) from hallucination can be difﬁcult, although illusions carry different aetiological and diagnostic implications.
and delusions as:
[A]bnormalities of thought rather than perception (although they may develop from the latter) and may be defined as ‘fixed false beliefs, strongly held and immutable in the face of refuting evidence, that are not consonant with the person’s education, social and cultural background.' [I]ts exact meaning and usage have evolved continuously, reflecting trends in psychology. Delusional themes commonly include: guilt, worthlessness, ill-health, persecution, reference, grandeur, love, jealousy, poverty, infestation, and religion. [...]
Regarding the difference between a hallucination and an illusion, which are the most closely related ones among the three, the Stanford Encyclopedia gives a clear-cut example, namely:
For example, when one has a visual experience as of a red object, it may be that one is really seeing an object and its red color (veridical perception), that one is seeing a green object (illusion), or that one is not seeing an object at all (hallucination).
- Elliot et al. Epilepsy Research (2009); 85: 162-71