What do the various terms tell us? Take the first term E = -q er/4p e 0 r 2. That, of course, is Coulombs law, which we already know: q is the charge that is producing the field; er is the unit vector in the direction from the point P where E is measured, r is the distance from P to q.
But Coulombs law is wrong. The discoveries of the 19th century showed that influences cannot travel faster than a certain fundamental speed c, which we now call the speed of light.
It is not correct that the first term is Coulombs law, not only because it is not possible to know where the charge is now and at what distance it is now, but also because the only thing that can affect the field at a given place and time is the behaviour of the charges in the past. How far the in the past? The time delay, or retarded time, so-called, is the times it takes, at speed c, to get from the charge to the field point P. The delay is r/c.