I can't say it any better than Wikipedia: Social return on investment (SROI) is a principles-based method for measuring extra-financial value (i.e., environmental and social value not currently reflected in conventional financial accounts) relative to resources invested. It can be used by any entity to evaluate impact on stakeholders, identify ways to improve performance, and enhance the performance of investments.
A network was formed in 2006 to facilitate the continued evolution of the method. Over 570 practitioners globally are members of the SROI Network.
The SROI method as it has been standardized by the SROI Network provides a consistent quantitative approach to understanding and managing the impacts of a project, business, organisation, fund or policy. It accounts for stakeholders' views of impact, and puts financial 'proxy' values on all those impacts identified by stakeholders which do not typically have market values. The aim is to include the values of people that are often excluded from markets in the same terms as used in markets, that is money, in order to give people a voice in resource allocation decisions.
Some SROI users employ a version of the method that does not require that all impacts be assigned a financial proxy. Instead the "numerator" includes monetized, quantitative but not monetized, qualitative, and narrative types of information about value.
I've also included a pdf which explains the crossovers with IRIS