"Post-bacc" classes are any classes that you take after you get your baccalaureate (aka, bachelor's) degree.
A post-bacc program is a program for people who want to go to usually either med or PA school, but who either didn't take the pre-req classes while in undergrad or did not do very well in them. Some programs offer degrees, some offer certifications. The post-bacc forum can give you more details.
I took some post-bacc classes after I graduated; I re-took orgo, and added on a couple graduate-level biology courses that looked like fun. I really liked my program b/c I could pretty much take whatever I wanted to take, but every school has different rules about it.