The power factor is the ratio between real power and apparent power. It is a generalization of the concept of cos φ. In case of a sinusoidal current, the power factor is just plain cos φ, but in case of non-linear current consumption (which is typical for phase-angle control and rectifiers, so a whole lot of electronic devices today), the power factor is affected by the current waveform as well.
Power grid operators prefer power factors close to one, because power is (by residential households) paid for real power, whereas the energy losses in distribution depend mostly on apparent power, so power factor compensation, the act of getting the power factor close to unity, is a great deal.
In the case of phase shift, the power factor can be brought to nearly one by just adding a parallel inductor or capacitor to the load, so that their reactive powers cancel out and just the true power remains as apparent power.
In case of non-sinusoidal current consumption, adding inductors or capacitors still is able to change the apparent power (and thus the power factor), but no amount of parallel inductors or capacitors can bring the power factor to one. So you can split the power factor into two parts: The displacement power factor is introduced by phase shift (called φ) and can be compensated using suitable reactance, while the distortion power factor is introduced by distortion and can not be compensated that way. The total power factor is the product of the displacement power factor and the distortion power factor.