Air pump and filter?

After reading through some posts somewhat related to my question I'm still unclear/confused about something. My question is does one need to use both an air pump and a filter in their aquarium? I am setting up a 20 gallon freshwater aquarium and am very early in the process. I have already gone and bought both an air pump (Tetrabrand rated 10-30 gallons) and a power filter (Marineland Penguin Pro 125) before discovering and joining this forum.