I made up this explanation for a non-electrical audience to understand the commercial value of having a high power factor but the core of the explanation is equally useful in other contexts:
The current flowing through cables transfers energy from supply to equipment like trains carrying coal from a mine to a factory. Ideally you want to completely load each train at the mine, send it to the factory full, completely unload it there and return it to the mine empty. This is what happens when the waveform of the current drawn by equipment is in phase (i.e. in sync) with the waveform of the grid voltage.
Suppose the unloading at the factory gets out of sync with the train movements and the trains leave the factory before they have been completely unloaded. The coal left on board goes back to the mine, then back to the factory, and so on back and forth. Because each train only delivers a part load, extra trains have to run to meet the demand. As far as paying for the coal, the factory still only gets billed for the amount it uses, but the transport costs are increased because of the pointless carrying of coal back and forth.
This is what happens when the current drawn by equipment is out of phase with the grid voltage. The current is not fully utilised in delivering real power (kW) to the equipment, instead being partially wasted carrying reactive power (kVAr) which consists of energy travelling back and forth. As far as paying for the energy (kWh), the customer still only gets billed for the amount it uses, but large customers have to pay for, or are penalised for, the extra reactive power (kVAr) to cover the supplier's cost for larger cables and transformers to transport the extra amps pointlessly carrying kVArs.
The power factor is the fraction of each train's payload that is actually unloaded at the factory, or the fraction of the supply current that delivers real power to the equipment. The lower the power factor, the less efficiently the transport mechanism is being utilised. A power factor of one indicates that the entire payload of coal is delivered or that all the current is utilised in delivering real power. A power factor of zero indicates that none of the coal is delivered, the trains are just running back and forth fully laden without any loading or unloading going on, and likewise a current flowing that delivers no real power.
To resolve any confusion between low pf and low efficiency:
Low pf is like wasting train journeys by sending some of the coal back to the mine. The coal itself is not wasted.
Low efficiency is like wasting coal by burning it in a heap in the yard instead of putting it into the boiler.