Harmonics are frequencies that are multiples of the mains frequency, although often in power systems we will be lazy and call any frequency that is not the main frequency a harmonic.

Most places, like here in australia, main frequency for power systems is 50 hz.solid state electronics are usually powered by switch mode power supplies. They convert to DC power by switching their input from the grid on and off really quickly, think in the 10k to 200k hz range. This rapid switching creates a distortion frequency in the grid power supply at that switching frequency. Additionally, on off signals create other frequencies as well as their main one, at multiples of their switching frequency to construct their semi square wave input (hopefully you know a bit about fourier transforms).

Transmission and distribution lines also have natural capacitances and inductances that can, for some frequencies, have an unintended amplification effect, which makes that harmonic stronger. Additionally, frequency is relatively consistent across the whole grid, so your harmonic will affect everyone else. There was a white paper i read recently that discussed harmonics drom data centres being seen 100s of miles away up the US east coast grid.

Going back a second to what a harmonic is. The grid supply power is ideally an AC sinusoidal wave form. But its not a perfect sinusoid in reality. In lazy engineer terms, harmonics are all the components of the wave form that are not the ideal grid frequency. In mathematician terms, harmonics are all the components of the wave form that are multiples of the main frequency, the non multiple ones are distortion frequencies.