How would society be different without limestone?

Answer 1

Here's a good link that talks about the most important benefit all life on Earth gets from limestone. Limestone locks up a lot of carbon dioxide (it's composed of calcium and carbon dioxide plus an extra oxygen atom- CaCO3). Without limestone, much of that carbon dioxide would be in the atmosphere causing extreme global warming. Here, I'll just copy the important part of article for you:

Limestone and the Carbon Dioxide Cycle

This cycle is very important. Without the carbon dioxide cycle, there would be no life on earth. We could not breathe. We would have no food. And without limestone, earth would be too hot for us to live. Instead, we have a nice climate. Animals and plants make the carbon dioxide cycle work.
Ocotillo plants in Arizona prefer to grow on limestone soils. Each year in the springtime, the ocotillos reach their red blossoms toward the sky. Hummingbirds come and pollinate the ocotillos. This helps these plants make seeds. The hummingbirds get to drink the sweet nectar of the flowers. But there's more to the story…

Ocotillos and all other plants make oxygen. Without this work, hummingbirds would not have any oxygen to breathe. Neither would we. Animals and people inhale oxygen. Then, animals and people exhale carbon dioxide. Plants use the carbon dioxide to build their stems, roots, and leaves. If the plants had no carbon dioxide, they would die. But there's more to the story…

Volcanoes also give off carbon dioxide. Between the animals and the volcanoes, a large amount of carbon dioxide forms. Fortunately, most of this carbon dioxide turns into limestone. If it did not, all the carbon dioxide would be in our air. This would make the earth very hot. Carbon dioxide traps heat. But limestone locks up harmful carbon dioxide. This makes our world cool enough to live in.

Answer 2

Limestone is a main ingredient in concrete and cement. We wouldn't have a lot of things without it.