Social entrepreneurs create organizations that operate like a business, but with a social mission.
This makes them different from the traditional non-profits, with the main difference being they attempt to create organizations that scale and become financially self-sustaining instead of relying on a non-stop stream of donations.
It's an exciting, growing field and a key reason the non-profit sector managed to grow through the Great Recession.
The Wall Street Journal has a good article covering the different legal structures social organizations can use to better accomplish their combined mission of social good with business practices.
These include the L3C, the Benefit Corporation (referred to as the "B Corp") and the Flexible-Purpose Corporation. Because of the legalities involved, I'm referring you to the article for more details.
Also, you should consult a lawyer or accountant prior to deciding what type of legal structure you want to form.
The growing availability and use of socially-oriented legal structures is a clear signal that social entrepreneurship continues to be on a growth trajectory.