Obamacare is the popular name for the Patient Protection and Affordable Care Act, an act which was created in 2010 to reform the U.S. health care system.
Obamacare requires everyone to have insurance and promised to make health insurance more affordable for the masses. It also pushes insurers to accept customers that they would have previously turned away for things like pre-existing conditions.
Read more about it—including both sides of the debate—here.