The relationship between cause and effect.
Causality (also referred to as causation, or cause and effect) is an influence by which one event, process, state or object (a cause) contributes to the production of another event, process, state or object (an effect) where the cause is partly responsible for the effect, and the effect is partly dependent on the cause.
(Based on Wikipedia.)
Causality can operate at several different levels. The lowest level, observation, is what traditional statistics measures. The middle level, intervention, involves examining what happens under forcing. The highest level is the counterfactual: what would have happened had something been different from the way it was?
In the New Causal Revolution, there are essentially two frameworks for investigation of causal effect: causal graphs a la Judea Pearl, and the potential outcomes framework of Donald Rubin. Both have their respective strengths and weaknesses.
