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 .
In a poset
A pair in a poset satisfies the covering relation if but there is no such that and . In other words, the interval contains exactly two elements and . In this case, you would say that “ covers ”.
In a directed graph
A pair of vertices in a directed graph or quiver satisfies the covering relation if there is an edge but there is no other path from to .
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.