It is a platform on which to build your own social network. Ning is a for-profit company that does some of the hard work involved with creating a social network. Mainly, they provide profiles, open ended data systems and a high degree of customizability. Ning allows developers to build apps in php by providing a number of classes that hook into their back end systems. You build the presentation and display logic, they handle the database and user work.
Note: We are not salesmen for Ning. We just think it's cool.