Philosophical presuppositions are ideas and beliefs we hold, consciously or unconsciously, which affect the way we interpret facts and evidence. In short, our philosophical presuppositions affect how we reason.
Many people are completely unaware of their philosophical presuppositions which is unfortunate since awareness of our philosophical presuppositions helps us better understand the arguments made by others who are often approaching a topic or subject from a completely different philosophical presupposition. Being aware of our presuppositions also helps us address the root of our differences with others rather than the outlying branches or surface issues.
Without addressing the fundamental differences in our world views what we end up managing to produce is more confusion and hard feelings than meaningful communication with others who hold fundamentally different presuppositions than we do.