If you perform satisfactorily on a quiz at school, it means you did it well enough to meet the expectations of your teacher.
Doing something satisfactorily means completing a task in a way that meets the required standards. It could involve submitting a project that covers all the minimally necessary points or cleaning your room so that it's neat and tidy enough to make your parents happy. The word satisfactorily comes from the Latin roots satis, meaning "enough," and facere, meaning "to make or do." So if you do your work satisfactorily, you do it well enough to meet the expected level of quality, fulfilling your responsibilities.