One more attempt to explain the apparent power:
The momentary power at a given time in an electric circuit is equal to the momentary voltage times the momentary current. This is not a definition, but follows from the definition of power, voltage and current. The momentary power is of little practical use in an AC-network, because the current and voltage are functions of time. It is better to calculate the average power over one cycle. It is equal to the rms voltage times the rms current times the cosinus of the phase difference between the voltage and current. That is, P = U I cos(fii), where P is the power, U is the rms voltage and I is the rms current, and fii is the phase difference. The cos(fii) is also called the power factor, pf.
Because cos(fii) appears in the expression of the power P, it is tempting

to define another quantity, Q = U I sin(fii). This is the reactive power. The apparent power S is then the vector sum of the power P and the reactive power Q, S = sqrt(P*P + Q*Q).
The reactive power and the apparent power do not have a direct physical interpretation. (I am afraid that the colleagues here might not agree with this view?) A load can generally be described as a resistance and an inductance in parallel. The power P is then the real, physical or “proper” power consumed in the resistance. It can be seen and felt as heat, mechanical power, etc. The reactive power is the “powerlike” quantity “consumed” in the inductance. It is related to the power that is oscillating between the load and the source.
The apparent power can be seen as the requirement for the maximum capacity of a transmission line. This can be seen in the following way: The voltage U in a network is more or less constant. Thus, if the power factor is low, then the current must be high in order to get the same power as with load having a higher power factor. The transmission lines must be capable of passing this current. The losses in the transmission lines are equal to the resistance times the current squared. (Again ,this is not a definition, but can be derived using Ohm’s law and the expression for power.) Because the losses depend on the resistance of the wires, not on the reactance, they do not “know” about the power factor. This means that the wires can be considered (and dimensioned for) to transmit a real power equal to the apparent power, but with a power factor equal to one.
The losses are apparently one of the reasons why the utilities do not like a low power factor, and why the power of the source must go up, when the power factor goes down.