The later part of the Carboniferous Period of the Paleozoic Era, from about 310 to 280 million years ago, is given the name "Pennsylvanian" in North America. European geologists do not make this distinction.
By about 310 million years ago, a range of mountains about where the Appalachian Mountains are today had mostly eroded away. A shallow tropical sea to the west1 of these mountains was mostly filled in by the debris. Frequent changes in sea level, alternately submerged and exposed the land, creating much thinner limestone and shale deposits than in the previous "Mississippian" period.
As the sea advanced and retreated, large tropical swamps migrated back and forth across the continent. Dead vegetation piled up in tremendous amounts, and the bottoms of the swamps were too anoxic to decay. Thus, the coal beds of North America and Europe were laid down. The lack of coal in the early Carboniferous and the abundance of coal in the late Carboniferous is the key motivation for American geologists' giving these two periods their own names.
By 280 million years ago, the supercontinent of Gondwana approached and collided with Laurasia, forming Pangaea and taking the Earth into the Permian period.
1 To the east of the mountains, there was also a shallow sea covering what is now Great Britain and Northern Europe. The coal beds of Europe were laid down at about the same time as the ones in North America, during the "Pennsylvanian" Period.