Distillation is about separating alcohol from water. Alcohol boils at a lower temperature than water and therefore when heated, the alcoholic vapours evaporate first and when cooled they condensate back into a liquid with a higher proportion of alcohol.
distillation is often achieved with stills (pot stills and column stills).

How does distillation work ?

Distillation is an old technique used to make alcohol, but also perfume, essential oil, or to purify water. This technique takes advantage of the different boiling points of different liquids. They will part from each other  when heated. They will condensate into a liquid form when cooled down, at different times, and this is the moment the distiller will seize to collect them separately. 

The distillate is usually collected in three moments starting with the foreshots (or the heads), followed by the heart and the tails (or feints). The different parts of the alcoholic liquid are called fractions. Each fraction has a different range of congeners. As ethanol is more and more concentrated the number of congeners falls, high strength spirits have less congeners and are lighter in character. Lower strength spirits have more congeners and are therefore heavier in character.

Most spirits are double distilled to achieve the desired alcohol level and some are even triple distilled such as Irish whisky or many many times distilled like some vodkas.

Depending on the type of spirit, the producer can either use a pot still or a column still to process to distillation, bother often made with copper.

why copper ?

Both still have a common point: they are made out of copper. Why ? The main reason is that copper is easy to  shape, conducts heat well and reacts with sulphur, removing it from the final spirit. It is also very beautiful and beauty matters.
Or in other words, this metal is chosen for its physical properties (malleability, good heat conduction) and its chemical reactivity with certain components of the distillate.

what are the main still in use ?

pot stills

Pot distilling is the most traditional way of distilling.
This is even hard to say when it was invented.

The pot is heated underneath, with different techniques involved (see the different kind of alcohol to understand the different techniques).
The pot still is indeed like a pot on legs. The form of the pot, quite large at the bottom narrows and curves when getting to the top (swan’s neck) over into a thin pipe called the worm.

The shape of the neck helps to separate the vapors. The worm is a coil that is then immersed into cold water. It is at this very moment that the alcohol vapour condensed into a liquid. 

During the  distillation a tool which looks like a little drawer located in the center of the process separates the heads (the first components evaporating) from the heart (good alcohol, also named ethanol) and the feints.

Distillation with pot still method often required two distillations to achieve a desired proof. The  heart (and tails, if heavier congeneers are desired to give additional taste) are distilled again.

column stills

Column stills are sometimes also called Coffey Stills or Patent Still. They have been invented in the wave of the industrial revolution (18th century) and are composed of two tall columns linked to one another.
 

The process is never interrupted like with the pot still. The liquid-to-distill has to go through the two columns until it becomes a finished distillate which can reach up to 95% abv.

The liquid is heated by vapour/steam and then cooled down descending through a succession of perforated plates in the first column (rectifier). The steam takes the alcohol out from the initial wash and carries it over to the second column (analyser) where it circulates until it can condense.

The succession of plates agglomerates certain types of congeneers at certain levels allowing the distiller to keep some to achieve a desired taste. The distiller is indeed able to judge in which trays different fractions of the distillation are and can run off the components he/she wants using a series of traps. Alternatively the distiller can continue the process until there isn't any fermented liquid anymore to feed in. Column stills allow more precision.
FROM A BUSINESS PERSPECTIVE ?
Pot still can have important size nowadays but it is never for industrial production, more for smaller operations.
It is still used as it allows creating difference between batches. This is where the marketing for pot still focuses.
FROM A BUSINESS PERSPECTIVE ?
This distillation technique allows vast amount of alcohol to be manufactured from the same base, to a high precision and sometimes purity but you can’t have different “batches” with particlar sensibilites and taste. Here the marketing will insist on the purity reached by multiple distillations.
The explanation starts at 1 min 40...