A linear load connected to a 50 Hz supply draws a sinusoidal current at 50 Hz. A non-linear load — variable speed drives, switched-mode supplies, LED lighting, arc furnaces — draws current in pulses, and that distorted waveform is mathematically equivalent to the fundamental plus components at 150 Hz, 250 Hz, 350 Hz and so on.
Those harmonics carry no useful power but they do generate heat: they overload the neutral in three-phase installations, raise losses in transformers and motors, trip protection with no apparent cause and degrade power factor correction capacitors. The third harmonic and its multiples are particularly troublesome because they add up in the neutral instead of cancelling.
Measurement is done with a power quality analyzer that decomposes the waveform and gives the amplitude of each order, normally up to the 50th. The reference standards are IEC 61000-4-30, which defines the accuracy classes, and EN 50160, which sets the limits allowed on the distribution network.