In logic, one proposition is a necessary condition of another when the second cannot be true while the first is false, and one proposition is a sufficient condition for another when the first cannot be true while the second is false. Thus, for example: “I have a dog” is a necessary condition for “My dog has fleas,” and “You scored ninety-five percent” is a sufficient condition for “You received an A.”
In causal relations, a necessary condition for the occurence of an event is a state of affairs without which the event cannot happen, while a sufficient condition is a state of affairs that guarantees that it will happen. Thus, for example: the presence of oxygen is a necessary condition for combustion, and the flow of electrical current is a sufficient condition for the induction of a magnetic field.1
1. Philosophy Pages.