The covering relation on a structure (generally already equipped with other relations) is a binary relation such that is related to if and only if is (in an appropriate sense) an immediate (and only immediate) successor of .
A pair in a poset satsfies the covering relation if but there is no such that and . In other words, there are exactly two elements such that : and . In this case, you would say that ” covers ”.
Given any binary relation on a set , a pair of elements of satisfies the covering relation if the only sequence such that satisfies (so ). Then the covering relation on a poset is the covering relation of , and the covering relation in a directed graph is the covering relation of the adjacency relation of the graph.