An Emergent Pedagogy is:

1.  A philosophy of teaching that is adaptive and responsive to the particular students in a class and the shifting social, cultural, and political context.

2.  A new way of thinking about teaching and learning that is grounded in theory but is also experimental in nature and, therefore, in need of a supporting research base.

Or, as Wikipedia succinctly puts it:

…a philosophy of teaching and a way of planning a children’s curriculum that focuses on being responsive to their interests. The goal is to create meaningful learning experiences for the children.

[emphases added]

As this page becomes developed, here are a couple of papers to review on the subject:

Emergent Pedagogy:

Learning to Enjoy the Uncontrollable

and Make It Productive

Emerging from the Deep:

Complexity, Emergent Pedagogy

and Deep Learning