One of the most important concepts in complexity science is that of emergence, which refers to the arising of novel structures, patterns, and properties out of antecedent/lower level interactions. Emergence has been observed across many different types of complex systems in a wide variety of scientific and mathematical fields. A closely related concept called self-organization can be explored here in an article written by Hermann Haken.  In social systems ranging from the scale of small groups through organizations through entire societies and cultures, emergent phenomena may appear differently in different types of systems, but they nevertheless share certain interrelated features that identify them as emergent:

a. Novelty: characteristics not previously observed and not predictable from knowledge of the interacting parts alone;

b. Coherence/correlation/integration: emergents appear as integrated wholes that tend to maintain intact identity over time. This coherence spans and correlates the separate lower-level components;

c. Global or macro level: since coherence represents a correlation that spans separate components, the locus of emergent phenomena occurs at a global or macro level, in contrast to the micro-level locus of their components;

d. Dynamical: emergent phenomena are not pre-given wholes but arise dynamically as a complex system transforms over time. Their dynamical nature has led to the use of dynamical systems theory to represent emergence, e.g., attractors, bifurcation/criticalization, control and order parameters, and so on;

In respect to strategies of scientific explanation, the construct of emergence is appealed to when the dynamics of a system seem better understood by focusing on across-system organization rather than on the parts or properties of parts alone.

In general, innovation occurring in social systems can be understood using the concept of emergence. Research into emergence is yielding many insights into those conditions which serve to foster innovation.

A set of downloadable papers and presentations on emergence authored by Jeffrey Goldstein can be found below.

References

Paper came out as "The Challenge of Organizational Innovation: Suggestions for Leaders from the Study of Emergence in Complex Systems," In S. Schloemer and N. Tomaschek (eds.). Leading in Complexity: A New Way of Management, pp. 24-39, Heidelberg, Germany: Systemische Forschung im Carl-Auer Verlag, 2009. pdf.

“Emergence, Creativity, and the Logic of Following and Negating,” The Innovation Journal: The Public Sector Innovation Journal, 10 (3), 2005, Article 31. pdf

“Emergence, Creative Process, and Self-transcending Constructions,” In Kurt Richardson (Ed.), Managing Organizational Complexity: Philosophy, Theory, and Application, pp. 63-78. Greenwich, CT: Information Age Press, 2006. pdf 

“The Construction of Emergence Order, or How to Resist the Temptation of Hylozoism,” Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 7, No. 4: 295-314. (2003). pdf

“The Singular Nature Of Emergent Levels: Suggestions For A Theory Of Emergence.@ Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 6, No. 4: 293-309. (2002). pdf

Emergence: A Construct Amid a Thicket of Conceptual Snares, Emergence: A Journal of Complexity Issues in Organizations and Management, Vol. 2, No. 1: 5-22. (2000). pdf

Emergence as a Construct: History and Issues, Emergence: Complexity Issues in    Organization and Management, 1(1), (1999), pp. 49-62. pdf