Secularisation Theory is the theory in sociology that as society advances in modernity, religion retreats and becomes increasingly hollow. Since the rise of science in the 17th Century, sociological commentators have realised that religion may be in a permanent decline, and some have proposed that science and intelligence, both rooted in the Enlightenment, are anathema to religious faith. Karl Marx (1818-1883), Durkheim (1857-1917), Max Weber (1864-1920), the founders of sociology, and William James (lectures from 1901-1902) are four eminent men who all noted this decline. The case was over-confidently stated by C.Wright Mills in 1959 who thought religion will decline and "disappear altogether except, possibly, in the private realm"1. It wasn't until the late 1960s that a coherent theory was developed, principally by "Berger, Luckmann, and Wilson, referring to processes developed by Durkheim (differentiation), Weber (rationalization), and Tönnies (Gemeinschaft-Gessellschaft)"2. The theory holds that intellectual and scientific developments have undermined the spiritual, supernatural, superstitious and paranormal ideas on which religion relies for its legitimacy, and, the differentiation of modern life into different compartments (i.e. work, politics, society, education and knowledge, home-time, entertainment) have relegated religion to merely one part of life, rather than an all-pervading narrative. As this continues, religion becomes more and more shallow, surviving for a while on empty until loss of active membership forces it into obscurity - although most theorists only hold this happens for organized public religion, not for private spirituality.
There is not a single definition of Secularisation Theory. The following are mostly very short descriptions for the purpose of showing quickly what type of thing this theory is. One very reasonable and oft-quoted definition by Bryan Wilson (1982) is:
“[Secularisation Theory is] that process by which religious institutions, actions, and consciousness, lose their social significance.”
But this definition is quite wide and includes most theories as to why religion is declining. It also specifically ties the description to social (public) significance. Whereas other sociologists such as Steve Bruce have collected data that proves that private religion is also declining4. Another definition by William Sims Bainbridge goes too far in stating that:
“[Secularisation Theory] in its simplest form holds that social and intellectual progress is rendering religion obsolete.”
"Atheism" by William Sims Bainbridge (2011)5
But few are far between are the brave anthropologists or sociologists who agree with the theory that religion will become obsolete! Bainbridge's piercing prediction doesn't correctly define the bulk of Secularisation Theory, just one extreme end of it. Roger Finke (1997) gives secularisation theory a more useful definition that doesn't concentrate on just social effects:
“[Secularisation Theory predicts] religion will decline as modernity erodes the demand for traditional religious beliefs.”
Roger Finke (1997)6
Here the word "traditional" takes into account the fact that it seems that new-age, individualistic and self-help religions are rising in popularity - although this rise is nowhere near enough to curb the overall downward trend in religious involvement. But "modernity" isn't the only element of secularisation that is causing this trend - or rather, it could be if you define it in the right way. It would be more useful if the definition included what it is about modernity that causes secularisation. One fuller description by an academic who has analysed various definitions' shortcomings arrives at this conclusion:
“[Secularisation Theory is a] process by which overarching and transcendent religious systems of old are confined in modern functionally differentiated societies to a subsystem alongside other subsystems, losing in this process their overarching claims over these other subsystems (... polity, economy, family, education, law, etc).”
"The Meaning and Scope of Secularization" by Karel Dobbelaere (2011)7
My initial instinct is to question the need for the word transcendent. There is no particular evidence that non-transcendental religions are less affected by secularisation - highly down-to-Earth and practical religions like Anglican Christianity are declining just as much as other established religions. Aside from that, the explicit mentioning of differentiation is a great element in Dobbelaere's approach.
Now it isn't fair to judge the relative worth of the above definitions as they are only tiny extracts of the authors' total work on the topic, and most are one-liners designed to give an initial feel, not a full definition. But they do serve to highlight some of the differences in opinion as to how far secularisation will go, and they do point you in the direction of the authors whom whose works you would read in order to understand Secularisation Theory.