The term "post-secular theology" is debated. Many theologians today think that Christian theology in modernity made a huge mistake in accepting to interpret the faith within the conditions of modernity (and this also apply to fundamentalist anti-reactions). But what it means to not accept the modern secularization is however disputed. I myself am influenced by two partly different perspectives: on the one hand John H Yoder's Anabaptist diaspora theology (which has made a great impact on such well-known theologians as Stanley Hauerwas) and on the other hand that "movement" labeled Radical Orthodoxy where you find theologians such as John Milbank and William Cavanaugh. But nevertheless, I think that the term is useful for several reasons and may open up for some interesting perspectives.
A post-secular theology doesn't see the idea of "the secular" as a neutral posture, but as an alternative (salvation) story which modernity, and maybe also post-modernity, convey. To speak about a secular sphere (e.g. the nation state) and a secular reason free form supposed religious influence is a confessional position. The secular modernity (the growth of which is a very complex phenomena, see e.g. Charles Taylor's A Secular Age or Talal Asad's Formations of the Secular) is in other words not a-religious, but deeply religious in its own way. From a Christian point of view it could - maybe a little provocatively - be described as a heresy and as a parody or travesty on the church and the gospel.
A post-secular theology doesn't recognize the split between secular and religious, and therefore neither (at least not in the way it has commonly been seen) between public and private (cf. the talk about religion as private), politics and religion, reason and faith, science and authority, facts and values.
A post-secular theology can be described as non-apologetic. It doesn't try to speak with our age by trying to show that there is a correlation between the gospel and certain cultural values (at least not in a systematic way), but rather to let the gospel in an attentive mode interpret and confront these values (you read the world into the gospel rather than reading the gospel into the world). A post-secular theology doesn't try to make the faith or the revelation reasonable or relevant in terms of something (supposed to be) universal. (In this sense I see Christian fundamentalism and evangelicalism - in their apologetic eagerness - to often be but a mirror of modernity!).
As I see it, a post-secular theology takes time (tradition, history, and the particular) seriously, in contrast to modernity which usually tries to go beyond time in its search for universal and a-historical principles and truths. This form of modernism you can see, for instance, in the way liberal theology reduce faith to universal moral principles, or in the fear of tradition which you can find in some versions of fundamentalism, or in such common phrases as "I believe in Jesus, but not in the church" or "don't let the tradition distort the radical message of Jesus in the gospels" or "Christian faith is simply about love – 'all you need is love'".
A post-secular theology also takes, from my perspective, space (the bodily nature of faith) seriously, in contrast to the tendency of modernity to reduce man to a "thinking thing" (Descartes). Such splits as those between body and soul, social/political/economical and spiritual, liturgy and freedom are extremely problematic. In other words: a post-secular theology doesn't accept modernity's individualization of faith. Because this individualization has led to a spiritualization of Christian faith (and religion in general) that has driven it to a non-bodily sphere and so it has lost its meaning for those things that fill most of our lives: material, social, political, and economical realities. Christian faith is something we can "touch", not just think about or feel in our hearts. When you in the name of modernity choose "non-religion" the opposite to spiritualization can also happen: only body is left, a "flat body" without depth. But from a post-secular perspective body and spirit belong together.
From my post-secular viewpoint I can't see the role of the church to be living in the margin that modernity and the nation state has provided. But at the same time I don't see it as a problem if the church is a minority or so to speak lives in "exile" or in "diaspora". On the contrary, it is maybe a necessary posture. Anyway, the social theology and practice of the church is not a part of the modern state project (with its talk about politics as pure statecraft), but is something which has its basis in the life of the church itself. The church doesn't just have certain values which may have political consequences, but the church is its own politics, its own sociology. The (first) task of the church is not to get the state to act in a more "Christian" way. Its first task is - with Jesus Christ as Lord - to be church, to see itself and its own social life as a social "project" which claims the whole existence and which is a part of God's mission in the world. As such the church can be "an alternative society and a positive counter-culture".