A connected component of an undirected graph is a maximal subset V' of the vertices with the property that every vertex in V' is reachable from every other vertex in V' (the maximal part means that there is no larger subset with this property). Any graph can be partitioned into its connected components by computing a DFS forest using DepthFirstSearch.
If the graph is directed, the analogous notion is a strongly-connected component (see StronglyConnectedComponents).