It's pretty common for someone to say, "You're deluded," when you believe something the other person doesn't believe. For example, if I were to say that I'm sure store-bought tomatoes are as good as home-grown, you might well tell me I'm deluded (or that I've never tasted a home-grown tomato).
However, if I believed home-grown tomatoes are dangerous because they contain microbes that attack the brain - microbes that are killed in store-bought tomatoes - and I went around to my neighbors' homes cutting down all their tomato plants every year - I would truly be suffering from a delusion.
Delusions are firmly held beliefs that are undeniably false. In bipolar disorder, delusions are one of the psychotic symptoms that may distinguish mania from hypomania.
A man who believes the CIA has targeted him, fills his house with booby traps, stockpiles food for a siege, is constantly checking for spy devices, believes his neighbors are agents who constantly watch him, etc., suffers from persecutory or paranoid delusions.
A woman who pesters or even stalks a celebrity believing she is his wife or lover is called a delusional stalker. This delusion is called erotomania (from Eros, the Greek god of sexual love).
A man who believes he has a special god-given power to control the weather has a religious delusion.
A woman who is sure she is the real Queen of England has delusions of grandeur.
Other delusions are things like believing one became a vampire after surgery (bizarre delusions) or receives special messages from radio or television broadcasts (delusions of reference). Other types exist as well.
Psychotic delusions are common in bipolar 1 disorder, schizophrenia, schizoaffective disorder and others. They may also be caused by physical conditions and illegal drug use.