You have to understand the concept of a Frame of Reference in order to understand Relativity of Simultaneity. In Einstein's Special Relativity, a scheme to create a coordinate system is defined in which you have three coordinates for specifying a location (x,y,z) and one coordinate for specifying time (t). Just like we have three coordinates for specifying a point in space, these four coordinates specify an event in the Frame of Reference. If you pick any two events and they have the same time coordinate, then they are simultaneous. If you then pick another Frame of Reference moving with respect to the first one, you can transform the coordinates for those two events using the Lorentz Transformation which will give you a new set of coordinates for the same two events. If the two time coordinates in the new Frame of Reference are equal to each other, then the events are simultaneous in that FoR. In general, two events that are simultaneous in one FoR will not be simultaneous in another FoR, but not necessarily.
So it has nothing to do with what is at rest or what is moving but simply the time coordinates of a pair of events in one Frame of Reference compared to another FoR.