It's a simple way to check changes in concentration of a chemical in water when you're not worried about external contaminants (i.e. just water vapor or anticipated chemical reactions).

For home brewers, measuring specific gravity at the start and end of your brew process is the simplest way to know how much alcohol is in your creation. For this you'd use a hydrometer: https://en.wikipedia.org/wiki/Hydrometer

It is a common way to measure battery charge through a hydrometer in automobiles batteries (not the sealed type):

https://en.wikipedia.org/wiki/Hydrometer

>Battery hydrometer

The state of charge of a lead-acid battery can be estimated from the density of the sulfuric acid solution used as electrolyte. A hydrometer calibrated to read specific gravity relative to water at 60 °F (16 °C) is a standard tool for servicing automobile batteries.

See also here:

https://deepcyclebatterystore.com/use-battery-hydrometer/