A class is a scheduled occasion where yourself and your peers meet with an instructor for a lesson. Classes can take many forms, but are typically one of: a lecture, a tutorial, a seminar, a laboratory, or a workshop.
When you class register, you are signing up to join others at a specific place and time. Where there are multiple classes to choose from, it means that it is the same lesson taught at different times or places. In this case, you would register to attend the one that best suits your schedule.