From: http://www.prodait.org/learning/threshold.php
What are threshold concepts?
A threshold concept is like a portal, opening up a new and previously inaccessible way of thinking about something. It represents a transformed way of understanding, or interpreting, or viewing something, without which the learner can not progress. As a consequence of comprehending a threshold concept there may be a transformed internal view of subject matter, subject landscape, or even world view. This transformation may be sudden or it may be protracted over a considerable period of time. The transition to understanding may prove troublesome.
Such a transformed perspective may represent how people ‘think’ in a particular discipline, or how they perceive or experience particular phenomena within that discipline (or more generally). It might, of course, be argued, in a critical sense, that such transformed understanding leads to a privileged or dominant view and therefore a contestable way of understanding something. This would give rise to discussion of how threshold concepts come to be identified and prioritised in the first instance.
Meyer and Land (2003) say that a threshold concept may be ‘troublesome’ because it is ‘alien’, or counter-intuitive, or even intellectually absurd at face value. It increasingly appears that a threshold concept may, on its own, constitute, or in its application, lead to, such troublesome knowledge.  Meyer and Land characterize a threshold concept as
- Transformative – once acquired it shifts perception of the subject
- Irreversible – once learners have come to see the world in terms of the threshold concept they can not return to their former, more primitive, view
- Integrative – acquisition of the threshold concept illuminates the underlying inter-relatedness of aspects of the subject
- Bounded – the threshold concept helps to demarcate subject boundaries
- Troublesome – a threshold concept may be far from ‘common sense’ understandings of the world and thus initially very difficult for learners to accept. In grasping a threshold concept the learner moves to a new perception of the world that may be in conflict with perceptions that previously seemed self-evidently true.
Erik Meyer and Ray Land develop these ideas in Occasional Paper 4: Threshold Concepts and Troublesome Knowledge