Most whiskey made in pot stills is either double distilled or triple distilled. The more times a spirit is distilled, the lighter and purer the final product is. Wood-aging can override the lightness of a spirit, though. For this reason, there is a delicate balance between fermentation and distillation in order for whiskey to contain aromatic elements without being smothered by woody characters. The shape, size, and material of a pot still influences whiskey flavor.
Pot stills are made of copper, a material that interacts with molecules to enhance the distillate profile. In general, pot stills create more robust distillates and often retain more raw ingredient flavor than other types of stills, which I'll get to in a minute. Much of the whiskey you love is distilled in what's called a continuous still, also known as a column. Column stills operator with the same goal as the pot still, to coax different aromatic flavors.