As a gravitational wave passes by the Earth, pulses will arrive early or late depending on whether space has compressed or stretched. If there are several pulsars in exactly the same direction in the sky, then all of the pulses from those pulsars will arrive early or late, and thus the arrival times are correlated. If the pulsars are not exactly in the same direction in the sky, but are separated by some angle, then the Hellings and Downs curve describes how correlated we expect the arrival times to be as a function of that angle.