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A delusion is a false belief that persists despite overwhelming evidence to the contrary.
In The Skeptic's Dictionary, the term is not used to designate a symptom of a psychiatric disorder. Generally speaking, beliefs I call delusions are those that I have found to be unchangeable by any quantity or quality of contrary evidence, vigorously defended by selective thinking, and apparently adhered to primarily for emotional reasons.
Obviously, people disagree as to what constitutes "overwhelming evidence," so when I use the word 'delusion' to describe belief in gods, spirits, psi, Scientology, etc., I am expressing a value judgment regarding the empirical evidence and logical support for those beliefs. I am not implying, however, that people who hold those beliefs are mentally ill or psychologically damaged.