Psychosis is the psychiatric term for delusions and hallucinations, with insight being the ability to recognise that what you believe or experience is not a fair representation of reality.
The concept of insight is more easily applied to hallucinations than delusions, after all you can hallucinate patterns on the walls but realise that the patterns are not really there, but you can’t really have a belief and not believe it.
With regard to delusions, it is tested by seeing how readily people can accept that there is a chance they might be wrong. In other words, it’s an estimate of certainty with absolute certainty in a false belief being considered abnormal.
In practice, and due to the difficulties on agreeing on or verifying reality, it often comes down to whether you agree with your psychiatrist (indeed, one definition of insight, includes accepting treating as a sign of good insight), sometimes leading to situations where people with genuine psychosis completely reject any form of treatment even where it would be of clear benefit.
Rachel Aviv’s article for The New Yorker is a brilliant exploration not only of the experience of slipping into psychosis but also the politics and practicalities of insight.
By the way, Aviv has written a series of excellent articles about mental health including one called ‘Which Way Madness Lies: Can psychosis be prevented?’ for Harper’s Magazine which is also online as a pdf.