Power quality is a term used to describe electric power that motivates an electrical load and the load's ability to function properly with that electric power. Without the proper power, an electrical device (or load) may malfunction, fail prematurely or not operate at all. There are many ways in which electric power can be of poor quality and many more causes of such poor quality power.
The electric power industry is in the business of electricity generation (AC power), electric power transmission and ultimately electricity distribution to a point often located near the electricity meter of the end user of the electric power. The electricity then moves through the distribution and wiring system of the end user until it reaches the load. The complexity of the system to move electric energy from the point of production to the point of consumption combined with variatons in weather, electricity demand and other factors provide many opportunities for the quality of power delivered to be compromised.
While "power quality" is a convenient term for many, it is actually the quality of the voltage, rather than power or electric current, that is actual topic described by the term. Power is simply the flow of energy and the current demanded by a load is largely uncontrollable. Nevertheless the relationship between the concepts of "voltage quality" and energy quality is unknown.

Introduction
It is often useful to think of power quality as a compatibility problem: is the equipment connected to the grid compatible with the events on the grid, and is the power delivered by the grid, including the events, compatible with the equipment that is connected? Compatibility problems always have at least two solutions: in this case, either clean up the power, or make the equipment tougher.
Ideally electric power would be supplied as a sine wave with the amplitude and frequency given by national standards (in the case of mains) or system specifications (in the case of a power feed not directly attached to the mains) with an impedance of zero ohms at all frequencies.
No real life power feed will ever meet this ideal. It can deviate from it in the following ways (among others):

Variations in the peak or RMS voltage are both important to different types of equipment.
When the RMS voltage exceeds the nominal voltage by 10 to 80% for 0.5 cycle to 1 minute, the event is called a "swell".
A "dip" (in British English) or a "sag" (in American English - the two terms are equivalent) is the opposite situation: the RMS volage is below the nominal voltage by by 10 to 90% for 0.5 cycle to 1 minute.
Random or repetitive variations in the RMS voltage between 90 and 110% of nominal can produce a phenomina known as "flicker" in lighting equipment. Flicker is the impression of unsteadiness of visual sensation induced by a light stimulus on the human eye. A precise definition of such voltage fluctuations that produce flickers have been subject to ongoing debate in more than one scientific community for many years.
Abrupt, very brief increases in voltage, called "spikes", "impulses", or "surges", generally caused by large inductive loads being turned off, or more severely by lightning.
"Undervoltage" occurs when the nominal voltage drops below 90% for more than 1 minute. The term "brownout" in common usage has no formal definition but is commonly used to describe a reduction in system voltage by the utility or system operator to decrease demand or to increase system operating margins.
"Overvoltage" occurs when the nominal voltage rises above 110% for more than 1 minute.
Variations in the frequency
Variations in the wave shape - usually described as harmonics
Nonzero low-frequency impedance (when a load draws more power, the voltage drops)
Nonzero high-frequency impedance (when a load demands a large amount of current, then stops demanding it suddenly, there will be a dip or spike in the voltage due to the inductances in the power supply line)