Reformed epistemology is a philosophical approach by Alvin Plantinga, William Alston and others, which broadly stated is: we have innate, God-given cognitive systems that provide direct, empirical experience which give us beliefs which require no reason - these are 'properly basic' beliefs. Beliefs are justified if they are properly basic. In addition, one has a 'sensus divinitatus', a sense of God, which provides direct access to God, which are justified, properly basic beliefs.
Critics of reformed epistemology argue that the divine sense is different from other senses, and that when we come to agreement about beliefs we generally come to a consensus with others - something that we can do when it comes to a group seeing a table or hearing a chime, but not for subjective religious experience.