In simple words, 'everything that happens, happens for a reason (or reasons) that explain(s) adequately why it happened'.
The kind of statement this is can be expressed as 'a rationalist view of a closed universe'. In an open universe, a cosmic ray from a far galaxy impacting on a neuron or transistor and causing actions to take place isn't a reason: it will be counted as noise. So, the principle implies no noise; it's all signal from a broad enough perspective. If you allow irrationalism as an active factor in the world, you can accept that markets 'behave irrationally', with consequences for us all. To argue against that you do have to introduce humans making the best sense they can from imperfect sources of information, market manipulation, their career prospects and so on.
The Principle was one of four recognised Laws of Thought, taught as such in pedagogic Logic courses for centuries (up to about 1910); the others being the Laws of Contradiction, Excluded Middle (these two go back to Aristotle), and Principle of Indiscernables (also Leibnizian - two individuals are identical if , and only if natch, they have the same attributes). With the new Logic of Frege and Russell and others, a serious research subject after a couple of millennia of slumber, these Laws became an embarrassing set of 'postulates' and were quietly dropped.
Went underground, is more like it. In the eighteenth century determinism (WikiPedia:FreeWill) was an live issue for intellectuals. For Leibniz, roughly speaking, the universe was closed, but only by using God (as a compactification, mathematicians would put it). The lesson of history is that 'contingent stuff happens'. Some argue that huge events are simply accidental: was there a reason sufficient to explain World War I, to take a favourite example? Sarajevo, yes - a reason, but sufficient? Leibniz handles contingency as based in infinitary reasons to which God has access. He also, as someone rooted in scholastic philosophy, took causality to be a multiplex concept too, in line with standard ideas that it was fourfold.
The philosophical atmosphere of the eighteenth century undertook to modernise this, leaving one with the 'clockwork universe' post-Newton: no God to do more than wind the clock (deism), no causality as high concept (Hume). The position reached on determinism is close to one familiar in the foundations of Cognitive Science in our days.
Determinism runs Sufficient Reason the other way round: not only does everything that happens, happen for a reason, but inescapably, since the reason necessitates the action. One can see this turn in action in currently-fashionable science-based theories. It is argued that neo-Darwinian evolutionary theory is a sufficient reason to explain highly-organised carbon-based life forms on planet Earth given a primordial soup. How deterministic is that? If you reproduce the soup and the physical conditions elsewhere, do you get alien life? It is convincing science that your DNA may encode factors affecting your health and behaviour. Is someone with a 'genetic disorder' really trapped in it? Would everyone with a gene disposing to heroin addiction, assuming one were found, end up as an addict? Clearly not: collapsing truth with certain kinds of 'necessary truth' misses a lot - specifically contingent factors in life, starting with the classic one, who your parents are.
The fascination with determinism returned in force with science fiction, as soon as it tried to be more than 'genre fiction': space opera with a 'grand narrative' behind it. The Asimov Foundation series has as a premise socio-economic determinism of a statistical kind ('psycho-history', complete with equations, just like Quantum Field Theory ...) In contrast the Dune books of Frank Herbert are based on talk about over-determined social and political conditions allowing for prescient forecasting of the future: too many reasons all pointing in one direction.
The interesting case for contrast is Tolkien: when Gandalf tells Frodo he was meant to have the Ring, but not by its maker, Gandalf is invoking a form of Sufficient Reason that would chime with any scholastic's understanding. Intention is assumed as a factor in the world. Since Tolkien's papers have been published we know that this way of thinking was part of his way of working, too, not added-on doctrine for the readers' benefit; one of the ways Tolkien differed from his fellow Inkling C.S. Lewis is that the whole elaborate system needed to conform (the Fall of Gondolin, one of the earliest fragments, needed a context in which the fall could be justified on tragic premises).
The place of the Laws of Thought hasn't really been filled since they lost their status (certainly for sufficient reasons, but still ...). Quantum theory negates Sufficient Reason while Relativity actually supported it by removing action at a distance. The various 'room' arguments (Schrodinger's Cat, Searle's Chinese) do seem to ask suspiciously similar questions to Sufficient Reason and Indiscernables, while the Laws themselves have a continuing if covert place in literature.
Very interesting, thanks.
(Comment on Asimov's world: but the Mule showed that the assumed postulates of psychohistory were incorrect and hence individual contingent events could impact history sometimes.)
Sure - the meticulously-planned scenario had to hit some snags or the series would have become dull. Also in the later volumes Asimov brought in the idea of robot intervention to shore it all up ... but hey, ScienceFiction isn't exactly rocket science. --CharlesMatthews