To presuppose is to take something as a given; presupposing is like assuming.
When you suppose something is true, you assume it's true; to presuppose means something similar. The pre — which means "before" — is a reminder that what you're assuming is background or pretext for something else. Asking “Want soup?” presupposes someone is hungry. Asking a woman "When is the baby due?" presupposes that she’s pregnant. Presupposing can be dangerous: if your presuppositions are incorrect, you could jump to the wrong conclusion.