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A Freudian slip, also known as parapraxis, is when you say one thing but mean your mother, er, another. It is a mistake allegedly committed by thoughts resting in the unconscious mind; it was suggested by Sigmund Freud in his 1901 book The Psychopathology of Everyday Life. A slip might occur in speech, in actions, in perception, in memory, etc.
Common examples include calling a co-worker "honey" when someone is unconsciously thinking they are talking to their spouse, or a child calling their teacher "Mom" or "Dad".
Freudian slips are semi-conscious, i.e. they're consciously repressed but unconsciously released.
The term is used popularly in order to humorously attribute hidden desires to the individual making the slip: saying something sexually suggestive when you meant to say something completely non-sexual is a great example. Several conservative politicians have slipped up in recent years using the words "colored" or "nigger" when they meant to say "Black" or "African American", suggesting a private, underlying racist worldview, long after those words have fallen out of acceptable use.