Electronic equipment (switching power supplies) draws current differently than non-electronic equipment. Instead of a load having a constant impedance drawing current in proportion to the sinusoidal voltage, electronic devices change their impedance by switching on and off near the peak of the voltage waveform. 
The circuit of the power supply only draws current from the AC line during the peaks of the voltage waveform, thereby charging a capacitor to the Peak of the line voltage.  The DC equipment requirements are fed from this capacitor and, as a result, the current waveform becomes distorted.
Switching loads on and off during part of the waveform results in short, abrupt, nonsinusoidal current pulses during a controlled portion of the incoming peak voltage waveform. These abrupt pulsating current pulses introduce  reflective currents (harmonics) back into the power distribution system. These currents operate at frequencies other than the fundamental 60 Hz.

The power supply in a modern personal computer is a good example of a non-linear load.   

Average response ammeters are only accurate when measuring 60 Hz loads that have sinusoidal current waveforms and cannot accurately measure the current of nonlinear loads. The reason is that nonlinear loads draw current in a nonsinusoidal manner, which produces reflective harmonic currents that operate above 60 Hz; both of these conditions are beyond the meter's design criteria. When an average response ammeter is used to measure nonlinear load current, the results can be inaccurate readings of as much as 25% to 50% the actual true-RMS current. As a result, the actual current of a circuit can exceed the rating of conductors and equipment. The actual current cannot be detected with the average-responding ammeter! 

When induction-disc watt-hour meters (Older power meters)  are monitoring non linear loads, depending on the content of the harmonics, the disk may run slower or faster, resulting in erroneous readings.  Many power companies are rolling out new True-RMS power meters to correct this.

In order to perform basic electrical trouble shooting for non-linear loads you must have an ammeter that provides true-RMS and instantaneous peak current ratings of the circuit. This meter must have the capacity of measuring the electrical characteristics of the waveform by sampling many points along the waveform. True-RMS meters are designed for just that, and they are accurate for both simple (sinusoidal) and complex (nonsinusoidal) alternating and direct current waveforms. Average response meters are only accurate with simple sinusoidal alternating current waveforms, ie lights, basic motors; not the complex waveforms resulting from nonlinear loads.

To say it bluntly, if your useing an average responding ammeter/ wattsmeter to get your readings you might as well make a lamp out of it because it is useless!

When a current, or voltage, operates at other than the fundamental 60 Hz frequency it is said to operate at a specific harmonic order (3rd harmonics operate at 180 Hz; 5th harmonics operate at 300 Hz).

Harmonic currents sometimes cause false circuit breaker tripping.   Peak sensing circuit breakers often will trip even though the amperage value has not been exceeded.   Harmonic current Peak values can be many times higher than sinusoidal waveforms.

Because reflective harmonic currents operate at frequencies higher than the fundamental, their effect in the electrical distribution system can be considerble. 
Odd number harmonics ( 3rd, 5th, 7th, etc. ) are of the greatest concern.   
Even number harmonics are usually mitigated because the harmonics swing equally in both the positive and negative direction.
The heating effect causes the greatest problem in electrical distribution systems and equipment.  Electrical equipment often overheats and fails even when operating well below the design ratings.   The increase in temperature is directly related to the increase in RMS current and the increased inductive heating effects of eddy currents, skin effect, and hysteresis.  (Increased eddy currents as transformers etc designed to cancel the 60hz frequency best)

On a note at Lan parties, which I help run serveral large events.
On balanced, three phase systems with no harmonic content, the line currents are 120° out of phase, cancel each other and result in very little neutral current.  However, at lans there is distortion all of the phase currents and almost 100% non-linear loads, the harmonic currents increase and the cancellation effect is lessened.   The usual result is the neutral current  is significantly higher than realised.   The triplen harmonics (odd multiples of three) are additive in the neutral and can quickly cause dangerous overheating.

In theory, the maximum current that the neutral will carry is 1.73 times the phase current and if not sized correctly, CONSIDERBLE overheating will result.   
A neutral burning off at a plug, or board can result in significant damaged equipment and has resulted in several dead pc's at one of my earlier events.
Once about 200amps per phase current is reached however the neutral drops to about 1 times phase current as some canceling of the 3rd harmonics takes place, thus only needs to be considered for the sub-boards.

Note: Written for 240v,60hz ac supply, but equaly applies to other's.