Before revision:  Hall's theorem gives a necessary and sufficient condition for a bipartite graph to have a saturating matching , meaning every vertex in one set is matchedto some vertex in the other in a one-to-one correspondence.
After revision:  Hall's theorem gives a necessary and sufficient condition for the existence of a saturating stable matching, where every agent on one side is matched , meaning every vertex in one set is matchedto some vertex in the other in a one-to-one correspondence.