I'm not a huge fan of nesting tables, but they do have some utility.
They're basically like side tables or reading tables or coffee tables, and they're used primarily in living rooms now, but originally they were used in sitting rooms/parlors/drawing rooms. When the room's not in use they remain stacked and out of the way. If you only have one or two guests, you can keep them stacked and they're still useful. If you have a lot of guests, then you can pull them apart, space them out, configure them however you like to suit the immediate need, and then re-stack them.
Their design intent is most definitely utilitarian. Their function is often somewhat less so.