What people call "Obamacare" is actually the Patient Protection and Affordable Care Act. However, people were calling it "Obamacare" before everyone even hammered out what it would be. It's a term mostly used by people who don't like the PPACA, and it's become popularized in part because PPACA is a really long and awkward name, even when you turn it into an acronym like that.
Anyway, the PPACA made a bunch of new rules regarding health care, with the purpose of making health care more affordable for everyone. Opponents of the PPACA, on the other hand, feel that the rules it makes take away too many freedoms and force people (both individuals and businesses) to do things they shouldn't have to.
So what does it do? Well, here is everything, in the order of when it goes into effect (because some of it happens later than other parts of it):