Here is one definition:
Social entrepreneurship describes the discovery and sustainable exploitation of opportunities to create social and environmental benefits. This is usually done through the generation of disequilibria in market and non-market environments. The social entrepreneurship process can in some cases lead to the creation of social enterprises. These social ventures are hybrid organisations exhibiting characteristics of both the for-profit and not-for-profit sector. Individuals engaging in social entrepreneurship are usually referred to as social entrepreneurs, a term that describes resourceful individuals working to create social innovation. They do not only have to identify (or create) opportunities for social change (that so far have been unexploited), they must also muster the resources necessary to turn these opportunities into reality. A typical example is Muhammad Yunus, founder of the Grameen Bank (Bangladesh) and recipient of the Nobel Peace Prize in recognition of his contribution to poverty alleviation through the invention and popularisation of microfinance.
Today many foundations aim to identify and promote social entrepreneurs. Two prominent examples are Ashoka and the Skoll Foundation. These so-called venture philanthropists adopt methods from the domain of venture capital, for example, encouraging social entrepreneurs to provide detailed business plans and to measure and report systematically on their social performance. Social return on investment (S-ROI) analysis is an example of an emerging tool aimed at describing the social impact of social entrepreneurship in dollar terms, relative to the philanthropic investment made.
Source: Credo Reference
Hockerts, K. (2007). Social entrepreneurship. In The A to Z of corporate social responsibility. Retrieved from https://libproxy.usc.edu/login?url=http://search.credoreference.com/content/entry/wileyazcsr/social_entrepreneurship/0
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Public websites that work with standards and performance metrics to measure the social, environmental and financial return on investments: