I personally haven't heard of this term before, but stumbled across this definition on the European Commission's website:

"Open Innovation 2.0 (OI2) is a new paradigm based on a Quadruple Helix Model where government, industry, academia and civil participants work together to co-create the future and drive structural changes far beyond the scope of what any one organization or person could do alone."

http://ec.europa.eu/digital-agenda/en/open-innovation-20

--------------------------------------------------
Note added at 16 mins (2014-11-26 22:24:55 GMT)
--------------------------------------------------

The term "Quadruple Helix (Innovation) Model" also appears to be used in the academic literature, building off of the "Triple Helix Model":

"The authors propose a theoretical growth model with which to frame analytically the Quadruple Helix Innovation Theory (QHIT). The aim is to emphasise the investment in innovation transmission mechanisms in terms of economic growth and productivity gains, in one-high-technology sector, by stressing the role played by the helices of the Quadruple Helix Innovation Model: Academia and Technological Infrastructures, Firms of Innovation, Government and Civil Society."

http://www.techrepublic.com/resource-library/whitepapers/a-g...

" In particular, they focus on the “Quadruple Helix” model,
through which government, academia, industry, and civil society are seen as key
actors promoting a democratic approach to innovation through which strategy
development and decision-making are exposed to feedback from key stakeholders,
resulting in socially accountable policies and practices. "
http://www.springer.com/cda/content/document/cda_downloaddoc...