With the end of the Devonian period about 359 million years ago, the Carboniferous period got started. Most of the land on Earth was warm and swampy, which was good for ferns, so that the continents were covered with big forests of ferns. When these ferns died, they formed thick layers of dead plants that eventually turned into coal. Most of the coal in the world today comes from ferns that grew during the Carboniferous period. So much carbon got used up making coal that there wasn't enough to combine with oxygen to make carbon dioxide, and instead the oxygen atoms had to just make oxygen molecules. Because of that, oxygen levels in the atmosphere rose much higher than before (and higher than they are now).
Plate tectonics caused the Euramerica continent to smash into Godwanaland, pushing the land up to make the Appalachian Mountains that run along the Atlantic coast of North America. Asia also ran into the other side of Europe to make the Ural Mountains. These are some of the oldest mountains that are still around today.
Although insects like spiders had already been living on land for many millions of years, now some of them began to fly like flies or dragonflies. Animals with backbones were just beginning to get started on land. These earliest animals, amphibians like frogs, had to go back to the ocean to lay their eggs. The frogs evolved to eat insects, because that was the only kind of land animal there was at this time.
But by about 310 million years ago, the climate was changing. It was getting much drier and hotter on land. So the plants and animals evolved to take advantage of that. Some early pine trees developed the ability to make seeds, so they could make baby pine trees even where there wasn't any water for their spores. And, in the same way, some of the amphibians developed into reptiles with the ability to lay eggs with hard calcium shells, so they could lay eggs on land in dry places and didn't need to stay near the water anymore.
The end of the Carboniferous period was about 290 million years ago, when the Permian period began.