Post secularism is an empty term that radical-apologists and hopeless post-modernists use with little agreement on what it actually means. What little can be universally gathered from the various near incomprehensible books written on the topic is that either secularism as it is/was is not the force of change and liberal tolerance as the "narrative" that secularists believe it is and that secularism is dying (or never really existed).
Continental philosophers[who?] claim that Habermas' and Charles Taylor's work on post-secularism is at the heart of debate on secularism in Europe. This is really not the case. Habermas and Taylor are at the centre of post-secularist debate while secularists and most religious people barely take note of what they say. However the post-secularist trope will not go away. For example a TEDx talk speaks of the post-secularist city while major liberal newspapers have reviewed both the previously mentioned books with incomprehensibly positive response.
Trying to make some sense of what it means
Most works use the term "secular extremism" as though this isn't an oxymoron. The cited cases of extremism are usually that of the French ban on Burqas and the banning of headscarves in Belgian public schools. While the secular argument claims that the use of Burqas both on one hand continue as an instrument of female oppression and religious subjugation and need to be stopped it also comes from the argument that full face coverings can be dangerous regardless if the coverings are of a secular or religious nature (someone walking around with a ski mask would be viewed with suspicion and perhaps stopped by the police). The post-secularist argument claims that the banning of the Burqa is, in fact an example of secular oppression forcing people to discard their sacred narratives, ancient dress codes and sense of dignity and modesty (rather than having women willingly or not, hide their bodily shame underneath a prison of fabric whenever out in public to avoid provoking men into raping them). They also argue that the claim of public safety is just an excuse to force religion to comply with the arbitrary world view of secularists who have already done so through the education system (censorship of religious views in educational material), politics (an overzealous application of the separation of church and state) and the shaming of religion as mostly fundamentalist and backwards. It should be noted that full Burqa use has been banned in some Muslims countries arguably to avoid suicide bombers using the disguise for ease of access to locations filled with civilians as well as opposition to what they see as a radical interpretation of Islamic dress code.
Another trope found in some post-secularist articles is a critique of the idea of secular progress as inevitable. While progress is not an essential feature of secularism (at least not the idea that progress is inevitable) it is attacked for several reasons. Progress is seen as an illusion and that progress for secularists is simply progress as secularists want it to be. Furthermore societies have always seen their ups and downs in social progress and secularism can never guarantee progress will continue indefinitely (though to claim so would be to admit that progress is in fact possible). Criticizing the secularist-mantra of progress is essentially a straw man (painting all secularists as idealists who believe that social and political progress is historical and constantly evolving into a freer better society). Many secularists would disagree that progress is historical, inevitable or even a chief aim of secularism. Instead the goal is a broader application of rights for all, greater use of reason in education and politics and the minimizing of religious influence in the public sphere. Progress is either a likely result of this or for others an illusion and besides the point.
Some post-secularists also claim that there is a resurgence of religion in the West and that some of it is fundamentalist (as a reaction to secularism). They disagree as to whether this is a good or bad thing. However the clear trend (at least in surveys) in the west shows an undeniable decline in religious belief and that fundamentalism in religion is isolated to protestant communities in English speaking countries (most notably the US and the UK) and to religious minority communities. Laws banning older religious based restrictions on social limitations (such as gay marriage, divorce, working on Sundays etc) are increasingly common in western countries as well. Perhaps fundamentalism isn't a forced reaction to secularism but rather a reaction to insane religious leaders and the lunacy of superstitious irrationality to begin with.
Indefinably is not a good thing outside of fiction
It has been claimed that the lack of a clear definition of just what post-secularism is one of its greatest strengths. This is common of most post-modern tropes (as well as most post-anythings). A lack of any clear definitions, wild disagreement, watery evidence, grand claims, and a non-rational framework are common in post-structuralism, post-feminism, post-humanism, post-blah-blah-blah and so on. It is most likely that post-secularism comes from religious thinkers (note our two authors are religious apologists) who lament the disappearance of certain oppressive Christian "values" from democratic societies and as a reaction to the decreasing amount of attention people pay to religion besides fundamentalist madness.