In the field of philosophy, an epistemic peer is someone who has an understanding of the world, or segment of the world, at broadly the same level as yourself.
There is a wide range of criteria used when defining an epistemic peer. Common criteria include equal access to evidence, equivalent cognitive abilities, equal education, equal reliability... and whatever else seems relevant. Often, peerage is limited to a specific area; for example, two physicists might be epistemic peers in their field, but not when talking about ethics or botany.
Theoretically, for simple ideas and facts, we should treat most people as epistemic peers until shown otherwise. For example, if Martin says that today is the 16th, and I think that it is the 15th, I might assume that we are both equally likely to be mistaken, and thus doubt the date... although I might still choose to date papers as the 15th, as I have no reason to chose his belief over mine. This disagreement certainly should influence me to double-check the date if possible. Of course, if Martin happens to be a five-year-old, or if I just checked the date a moment ago, I should give more weight to my own opinion.
Most matters that we apply epistemological theories to are significantly more complex than today's date. Identifying an epistemic peer in the field of religion, ethics, or epistemology is a non-trivial task. Some people, when faced with hypothetical questions about epistemic peers, fall back on the claim that the term is nonsense, because no two people share exactly the same culture, upbringing, education, etc. This is of course true, but also pointless and missing the point, like refusing to use the word 'big' because there is no formal definition that delineates exactly what is big and what is not; epistemological peers are a useful concept, even if the term is not perfectly precise.
Perhaps the most useful definition of an epistemic peer is someone whose way of thinking you trust enough to take disagreement seriously. If you do not have someone who meets this definition and do not think that it is likely you could find one, you should probably be seriously questioning your epistemology.