The first place you should look is
http://www.wikipedia.org; search for 'reactive power'.
There are contributors to this site who will insist that reactive power doesn't "flow", or that there's no such thing as reactive "power". But for the purposes of this contribution (and per commonly acepted convention--see
http://www.wikipedia.org) we will consider that reactive power does indeed exist and that it flows. And remember: the originator of this thread asked for an explanation in layman's terms, which for me, anyway, does not initially include vector diagrams and trigonometry and mathematical formulae. All of these things are necessary for a complete and proper understanding of the phenomenon, but not for a rudimentary understanding on which to base all of the formulae and vector diagrams, etc., which just serve as mathematical proofs of the principles.
In an AC power system, there are resistive loads and reactive loads. Reactive loads include inductive and capacitive loads--and the majority of loads on any grid are inductive (from induction motors used for everything from vibrators to elevators to refrigeration compressors to fans to all manner of pump motors (potable water, sewage, chemical, and so on)). Transformers are also an inductive load on the system.
So, since they're the predominant load, let's focus on inductive loads. In an induction motor, a magnetic field has to be induced on the rotor of the motor in order for it try to follow the apparently rotating magnetic field of the stator that is connected to the AC power source in order to produce torque. The act of inducing the magnetic field on the rotor of the induction motor causes a shift to occur between the AC current sine wave and the AC voltage sine wave of the AC power system. Some of the total amount of energy that's being consumed from the AC power system by the induction motor is used in the induction of the magnetic field on the rotor of the motor whiach allows the motor to produce torque. In other words, the total amount of energy being consumed by the motor does not end up as torque (real power).
The magnitude of the shift between the AC voltage- and current sine waves is measured or expressed in many ways: power factor, VArs, phase angle, etc.
The key thing to remember is that if nothing is done to try to contain or reduce the phase shift between the AC voltage- and current sine waves they can eventually shift so much that the ability of the AC system to supply real power will be reduced (such as when brownouts occur).
If we think of the induction of the magnetic field on the rotor of the induction motor as needing "power" and we call that reactive power, then we can think of reactive power as being consumed, in the same was as real power is consumed. We can measure the amount of power required to induce the magnetic field on the induction motor rotor in VArs. And, to counter the effect of the phase shift on the system of lots and lots of induction motors and transformers (which also induce magnetic fields on secondary windings) we can produce reactive power to reduce the phase shift and maintain the AC power system's ability to provide power.
We can produce reactive power to "compensate" for the inductive load on the system primarly by increasing excitation current to the rotors of synchronous generators over and above the amount required to maintain the generator terminal voltage equal to the voltage of the grid to which the generator is connected. This causes reactve power, called VArs to flow out of the generator terminals on to the AC power system, reducing the phase shift and supporting the AC power system's ability to transmit real power.
So, VArs are "required" or "consumed" to induce the magnetic field on the induction motor rotors commonly used everyhwere, and to increase or decrease voltage through transformers used to distribute AC power. The effect of VARs on the system is to shift the AC voltage- and current sine waves out of phase with each other. If they get too far out of phase, the ability of the AC power system to supply power is reduced. VARs can be produced by synchronous generators--but since that requires DC power, and that DC power usually comes from the AC power system, that power is not available for sale to consumers. Power factor correction capacitors can be used to help with controlling the phase angle between the AC voltage- and current sine waves, but they are usually expensive and have their own idiosyncracies.
Real power, watts, can be converted in to torque and work which is something we can understand and visualize. Reactive power, VArs, have no such tangible quantity that we can see or envision. A lot of people like to say that, "VArs are like foam on beer; it's just there but it doesn't do anything." Foam on a beer tells the drinker the beer is not flat. There's very little worse than a cold, flat beer especially on a hot day.
Okay, a hot, flat beer is worse. And if AC power systems aren't properly managed, the beer could be flat and hot.