retrocausality assumes that influences can travel backwards in time. When an experimenter decides how to measure a particle, that choice can influence the properties of that particle — or, an entangled particle in the past. This, therefore, makes the “action at a distance” part of Einstein’s definition unnecessary. Instead, the entanglement effect becomes retrocausal influence. That being said, it’s not the same thing as sending signals back in time.
The appeal of retrocausality
First, to clarify what retrocausality is and isn’t: It does not mean that signals can be communicated from the future to the past—such signaling would be forbidden even in a retrocausal theory due to thermodynamic reasons. Instead, retrocausality means that, when an experimenter chooses the measurement setting with which to measure a particle, that decision can influence the properties of that particle (or another particle) in the past, even before the experimenter made their choice. In other words, a decision made in the present can influence something in the past.
In the original Bell tests, physicists assumed that retrocausal influences could not happen. Consequently, in order to explain their observations that distant particles seem to immediately know what measurement is being made on the other, the only viable explanation was action-at-a-distance. That is, the particles are somehow influencing each other even when separated by large distances, in ways that cannot be explained by any known mechanism. But by allowing for the possibility that the measurement setting for one particle can retrocausally influence the behavior of the other particle, there is no need for action-at-a-distance—only retrocausal influence.