The Black Swan Theory is used by Nassim Nicholas Taleb to explain the existence and occurrence of high-impact, hard-to-predict, and rare events that are beyond the realm of normal expectations. Unlike the philosophical "black swan problem", the "Black Swan Theory" (capitalized) refers only to unexpected events of large magnitude and consequence and their dominant role in history. Such events are considered extreme outliers.
It is noteworthy that in his writings, Taleb never uses the term, "Black Swan Theory", instead, he refers to "Black Swan Events" (capitalized).
Black Swan Events were described by Nassim Nicholas Taleb in his 2007 book, The Black Swan. Taleb regards almost all major scientific discoveries, historical events, and artistic accomplishments as "black swans"—undirected and unpredicted. He gives the rise of the Internet, the personal computer, World War I, and the September 11, 2001 attacks as examples of Black Swan Events.
Use of the term, a black swan (not capitalized), is derived from the seventeenth century European presumption that 'all swans must be white', because all historical records of swans reported that they had white feathers. In that context, a black swan was something that was impossible, and could not exist. After the discovery of black swans in Western Australia  during the eighteenth century, the term metamorphosed to connote that a perceived impossibility, later may be found to exist. Taleb notes that, writing in the nineteenth century, John Stuart Mill used the black swan logical fallacy, as a new term to identify falsification.
Writing in the New York Times, Taleb asserted, "What we call here a Black Swan (and capitalize it) is an event with the following three attributes. First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable. I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability. A small number of Black Swans explain almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives." 
The main idea in Taleb's book is not to attempt to predict Black Swan Events, but to build robustness into negative ones that occur and being able to exploit positive ones. Taleb contends that banks and trading firms are very vulnerable to hazardous Black Swan Events and are exposed to losses beyond that predicted by their defective models.
Taleb states that a Black Swan Event depends on the observer—using a simple example, what may be a Black Swan surprise for a turkey is not a Black Swan surprise for its butcher—hence the objective should be to "avoid being the turkey" by identifying areas of vulnerability in order to "turn the Black Swans white".
Based on the author's criteria:
Taleb's black swan is different from the earlier philosophical versions of the problem, as it concerns a phenomenon with specific empirical and statistical properties which he calls, "the fourth quadrant". Before Taleb, those who dealt with the notion of the improbable, such as Hume, Mill, and Popper focused on the problem of induction in logic, specifically, that of drawing general conclusions from specific observations. Taleb's Black Swan Event has a central and unique attribute, high impact. His claim is that almost all consequential events in history come from the unexpected—yet humans later convince themselves that these events are explainable in hindsight (bias).
One problem, labeled the ludic fallacy by Taleb, is the belief that the unstructured randomness found in life resembles the structured randomness found in games. This stems from the assumption that the unexpected may be predicted by extrapolating from variations in statistics based on past observations, especially when these statistics are presumed to represent samples from a bell-shaped curve. These concerns often are highly relevant in financial markets, where major players use value at risk models, which imply normal distributions, although market returns typically have fat tail distributions.
More generally, decision theory, based on a fixed universe or a model of possible outcomes, ignores and minimizes the effect of events that are "outside model". For instance, a simple model of daily stock market returns may include extreme moves such as Black Monday (1987), but might not model the breakdown of markets following the September 11 attacks of 2001. A fixed model considers the "known unknowns", but ignores the "unknown unknowns".
Taleb notes that other distributions are not usable with precision, but often are more descriptive, such as the fractal, power law, or scalable distributions and that awareness of these might help to temper expectations.
Beyond this, he emphasizes that many events simply are without precedent, undercutting the basis of this type of reasoning altogether.
Taleb also argues for the use of counterfactual reasoning when considering risk.