Marginal analysis is a type of cost-benefit analysis. It looks at the costs and benefits that a person or firm will experience if they take some particular action. Marginal analysis asks "how much more will it cost me to do x" and "how much more will I gain from doing it." If the gain is more than the cost, you should do whatever "x" is.
For example, let's say you've been studying economics for 2 hours and you have a test tomorrow. You want to decide whether you should study another hour. You have to ask yourself how much another hour of study will improve your grade (marginal benefit) and compare that to how much that next hour of study will tire you out or frustrate you (marginal cost). If the benefit outweighs the cost, you keep on studying.