Wikipedia succinctly defines postmillennialism as "an interpretation of chapter 20 of the Book of Revelation which sees Christ's second coming as occurring after (Latin post-) the 'Millennium', a Golden Age or era of Christian prosperity and dominance."
Many of us who have encountered evangelical Christianity are more familiar with premillennialism: the idea that Christ's second coming will predate the eventual establishment of the Millennium. In this kind of thought, Christ is typically imagined as appearing during a time of great tribulations (as every historical era, including our own, imagines itself to be) and rapturing the faithful up into heaven - leaving behind the unbelievers. However, there are many variations on the theme: some premillennialists imagine a time of even worse tribulation after the second coming; different thinkers draw on different theological traditions dating back to ancient times; and so on.
There's a huge body of best-selling Christian literature that explains or exploits premillennialist ideas, most famously the novel Left Behind and its sequels. When I was young, Hal Lindsey's The Late, Great Planet Earth was a popular premillennialist text. I was taught in Sunday school that the second coming was likely to be in the 1980s, a "generation" after the recreation of Israel. Pity it didn't work out like that.
Postmillennialists see a duty to reform society along Christian lines to build the utopian age that is, as they understand it, prophesied in the Bible - particularly the Book of Revelation. Since they want to usher in this utopian age by human efforts, theirs is an eschatology of works and progress. It's easy to see that Nazism and Marxism contained concepts of history closely analogous to this - but it is too clever by half to say that these belief systems just are postmillennialist. They are not, because they don't have anything to say about the the second coming of Christ at the end of the millennium. Though they envisage apocalyptic events, posit quasi-religious views of the unfolding of history, and are clearly influenced by Christian thought, they are not themselves Christian sects.
It is even more strained when any system of thought at all that envisages progressive improvement in the human situation is labeled postmillennialist, as if any such ideas make sense only in the context of Christian religious doctrine. Though Christian views of history may have made it easier to imagine a direction to history, we have another very good reason to do so: the observable facts of scientific and technological change, with their implications for society. Whatever else we might think about progress, science really does gain greater insight into the nature of our world and technology really does become more powerful. Somebody who thinks that we can use the increasingly powerful science and technology at our disposal to improve the human condition does not need to be motivated by religion. Nor does the plausibility of her position stand or fall with the plausibility of religion itself.
That's an important point to make, because critics of technological meliorism (in its various guises) often adopt a kind of world-weary cynicism, in which technological meliorism is dismissed as just another kind of religion, and just as likely to be wrong as the supernaturalist doctrines of real religions. That's clearly a mistake.
These people could make a much weaker claim: one that is far less ambitious but more likely to be correct. This is the point that, after two thousand years of Christianity, we have become primed to see history as having a direction, and some folks may have become over-optimistic (both about what will happen and about their capacity to predict it). Perhaps this is right, but the fact remains that we have a perfectly rational, independent basis to expect further improvements in science and technology and to be able to use them to produce improvements to, say, human health and comfort and the human life span.
Transhumanist thinking is particularly vulnerable to the suggestion that it is something like apocalyptic Christianity - and therefore just as likely to be false. But that argument is just wrong. The most that can be said is that the apocalyptic aspect of the most extreme kinds of transhumanism may have a psychological appeal - for some people - that is out of proportion to the strength of its actual arguments. I don't doubt that there's some truth in that claim, and that it provides a reason to examine transhumanist arguments of an extreme kind (such as those predicting a near-future technological Singularity) with a degree of scepticism. Nonetheless, the arguments ultimately stand or fall on their own merits, not on the merits of Christian doctrine.
It's particularly annoying when Michael Ruse (in The Evolution-Creation Struggle)wants to brand any progressive element in the thinking of modern scientists as postmillennialist. No! No, Professor Ruse, postmillennialism is a doctrine (with a number of variants) taught by some Christians. But you don't need to be a Christian of any sort to believe that science and technology are becoming more powerful, or to plan ways of using them in an attempt to improve the human condition. There are non-religious reasons to be impressed by the advance of science and technology. Accordingly, the postmillennialist/premillennialist contrast that Ruse relies on in examining the clash between evolution and creationism is unnecessary and misleading.
I am actually a sceptic about the supposedly coming technological Singularity, an idea that Ruse doesn't get around to discussing. It looks just as likely to me that we are somewhere on the steeper part of a technological sigmoid curve - but who knows? My point is that you can't shoot down arguments, such as those of transhumanists, by drawing an analogy with a quite different set of ideas that is based on a quite different set of arguments ... arguments that you believe to be bad.
More generally, you can't do the following. You can't take a way of thinking, X, that bears some superficial resemblance to another way of thinking, Y, which is grounded in a quite different set of arguments ... then observe that way of thinking Y is religious (and is grounded in whatever arguments support the religion), and conclude that way of thinking X is religious (implying that it stands or falls with the general plausibility of religion). I see far too much of this kind of fallacious reasoning, and it's starting to get annoying.