A nonprofit organization is an organization formed in order "to pursue a common not-for-profit goal", that is, to pursue the stated goal expressly without the intention of distributing excess revenue (i.e. profit) to members or leaders. Nonprofit legal structure will often have taxation implications, particularly where the nonprofit seeks income tax exemption, charitable status and so on.
The terms nonprofit and not-for-profit are not consistently differentiated across jurisdictions. In layman's terms they are usually equivalent in concept and common usage, although in various jurisdictions there are accounting and legal differences.
-adapted from Wikipedia: Nonprofit organization.
Nonprofit housing organization 
(for development organizations specifically, see Community Housing Development Organizations section below).
National Center for Healthy Housing
National Housing Institute - http://www.nhi.org/, founded 1975.
publishes quarterly magazine, Shelterforce, and community development blog, Rooflines.
Community Housing Development Organization 
(a term of art used by HUD, etc).
comment from Sam Moss: "Local NP Affordable Housing developers separated from state wide separated from country wide developers might be worth listing. I'm finding more and more how much that one fact leads to different political views and development goals."