A **formal context** K is a relation between the objects O and attributes A. It indicates which attributes apply to which objects. It is represented by a bipartite graph.
A formal concept C is a special kind of sub-relation of K, corresponding I believe to a maximal complete bipartite subgraph.
That is, it is a subset \\(X\\) of the objects along with a subset \\(Y\\) of the attributes, such that every object in \\(X\\) has all the attributes in \\(Y\\), and \\(X\\) is maximal in this regard.
Note this is not the standard formal definition, as presented in _op. cit._, Wikipedia, etc., but I believe it is equivalent.