"Flukes" are rare, exceptionally successful performances of an action. They are currently most well known for occurring with certain defensive spells, including Mama Kolydina's Instant Infestation and Transcendent Pneumatic Alleviator (TPA). It is not known if they are limited to spellcasting, though there are at least similarities with some specials, such as the Vetinari inhume.
That a fluke has occurred is not necessarily immediately obvious, such as with TPA where the successful casting looks the same as any other, but can become self-evident over time when the spell's effects are clearly much more powerful and long-lasting than normal. With TPA, for example, even a powerful wizard's normal castings last only on the order of hours and can absorb only a few thousand HP of damage at a time, but a fluke version can last for days and is virtually impervious.
Flukes are exceedingly rare, and many players might never witness them.
Flukes are sometimes also referred to as "perfect casts" (for spellcasting, specifically).
The underlying criteria for achieving a fluke is not known, but is speculated to involve achieving maximum scores on every skillcheck involved in the action. Given there are random elements ("rolls") involved in most skillchecks, this is always unlikely even at very high skill levels. Though, if that speculation is accurate, then flukes will be more likely to occur for more skilled players.
Unfortunately, their inherent rarity makes reverse-engineering the mechanism very difficult. Please contribute to the research page if you experience a fluke.