Foundationalists believe in logical, ordered opinions, built on other opinions. Building ideas is like building a house - you have to start at the most basic truths, and work your way up from there, otherwise it simply doesn't work. Thus, a foundationalist's entire goal is to find a single universal truth, that cannot be refuted by any argument. Once that truth has been found, everything else can fall into place. "I think, therefore I am" is often argued to be one of these basic truths.
Famous foundationalists include: Rene Descartes.
The opposite of Foundationalism is Realism.