Popper attributed to Plato the idea that we divided apparent knowledge into two classes : doxa (or mere superstitions, ungrounded beliefs), and episteme (rational, typically justified beliefs.)
This view of rational knowledge as being justified still dominates today. (Sometimes using the definitional formula that knowledge is justified, true, belief). Beliefs are rational when we have reasons for them. We believe A because it follows, or is deducible from, B and C.
But there is a problem with this view : it seems to require an infinite regress. If it's rational to believe A because it follows from B, and B because of C etc. don't we need an infinite chain of antecedent beliefs?
Or, if we want to avoid this regress, we must stop it somewhere and say that some beliefs are grounded or justified by foundational beliefs which are not themselves further justified. (In which case, what makes them rational?)
Or that some kind of circularity takes place :
Typcially, epistemologists try to make sense of one of these positions; and arguments rage between foundationalists, circularists; and naturalists who challenging the very idea of a philosophical notion of rationality.
See Wikipaedia for more on this regress discussion : http://www.wikipedia.org/wiki/The_regress_argument_in_epistemology
Popper's response is radical. Given that none of the variants are attractive, he chooses to break the connection between justification and rationality. In his terminology, one can not judge knowledge by its "pedigree". In other words beliefs are not rational in virtue of their justifications.
This does not make Popper a naturalist or sceptical rejector of rationality altogether. (IsPopperNaturalist?) Instead he defines an alternative : CriticalRationalism. This is a notion of rationality as a property, not of individual beliefs, but of agents (or, it may be thought, of research programs or communities) and should be understood as a disposition or even ethic.
Next : CriticalRationalism