Fusel oils
Also known as: higher alcohols, fusel alcohols, fuzle
Alcohols with molecules larger than ethanol — mainly propanol, isobutanol and the amyl alcohols. They form during fermentation, as a by-product of yeast working on amino acids.
They boil above ethanol, so they evaporate later and collect in the tails. Cutting the end of the run is the simplest way of getting rid of most of them.
The body breaks them down more slowly than ethanol, and what the breakdown leaves behind is harder going. Hence the repeated observation that badly cut moonshine gives a headache that feels different, and lasts longer, than one from clean vodka.
They are not always a fault, though. In whisky, rum and fruit brandies some of the higher alcohols and esters are kept deliberately — they are the aroma. That is why those spirits are distilled to a lower strength than rectified spirit, which is meant to be neutral. The line between "impurity" and "character" runs through quantity, and through what you want from the spirit.
There will be fewer fusels if fermentation runs cooler, on distilling yeast rather than baking yeast, with the mash properly fed — and if you cut the tails decisively rather than "just a little more".