It depends on the humidity of where you’re at. On a warm day in Houston, for example, it’s not at all uncommon for water to condense on the outside glass of a cold drink, run down, and eventually damage the wooden table it’s sitting on. A coaster will help prevent that damage.
They’re to prevent condensation from pooling on the table itself. This can warp or otherwise mess up a wooden surface. On other materials it can just leave ugly rings that you have to clean off.
Also to prevent hot drinks effecting the surface finish of said table via temperature effects etc.
In addition to the condensation, I have also used coasters for under hot drinks like coffee as they can discolor or even deform some surfaces.
If all you drink is room temp liquids you don’t need coasters.
What’s the movie/short story called again?
Arrival
The short story version is called Story of Your Life by Ted Chiang