MOOC stands for Massive Open Online Course. The MOOC is simply a scalable method of free online study (although revenue streams have been put in place in most of the big MOOC providers now). A MOOC is usually a partnership between a 'traditional' university (which brings the content) and an online provider, which brings the delivery mechanism and, eventually, the audience. Confusingly, a few of the big MOOC providers were originally set up by traditional universities (eg edX was set up Harvard and MIT), primarily to extend their brand into the online market, but now these providers also feature courses from many other universities too. Technically the first MOOC was created in 2005, but really the proliferation and development of this from of online learning happened in 2012.
Examples of big MOOC providers are Coursera, edX, Udacity, The Khan Academy, and the UK-based Futurelearn.