If you pass steam through plant material, it will collect some of the aromatic substances that are in the plant. Some of these substances dissolve in water, and some don't. And when the steam is cooled down and turns back to water, the non-water-soluble 'oily' substances quickly separate out from the water (like oil and vinegar). These substances collectively create the plant's essential oil.
However there are many water soluble plant products which end up in the water, and this water is known as a 'hydrolat' or 'hydrosol' (there is absolutely no difference, just the terminology). Hydrosols are highly therapeutic in their own right.
It is not true to say that the hydrosol is the 'by-product' of the distillation process. Many distillers will distill purely for the hydrosol and will set everything up for this to be the end product.
Hydrosols have a delicate nature and a light aroma. They are ideal for situations that require gentle aromatic care, and can be used especially for children, the elderly, the highly sensitive, and those who are very debilitated by illness.