Geology helps to explain why hikers can see a vista of mountains from the top of Dragon's Tooth near Roanoke, why the Chesapeake Bay Bridge has two tunnels... and why the western part of the state is mountainous but the eastern part of Virginia is flat.
Obviously, Virginia is on the eastern edge of the North American continent - but we are not on the eastern edge of the North American tectonic plate. Virginia is closer to the middle of the tectonic plate than to the eastern edge. The eastern edge of the tectonic plate is the Mid-Atlantic Ridge, in the middle of the Atlantic Ocean. The western edge is the San Andreas fault on the California coast.
There are constant earthquakes on the edges of the plate, where rock is oozing up to the surface (in the Mid-Atlantic Ridge) or rubbing against other plates (in California). Since Virginia is near the center, friction against other plates is minimal here - that's the main reason Virginias feel so few earthquakes.

Virginia wasn't always where it is today. Plate tectonics theory says we're moving west towards Japan at maybe one inch (2.5cm) per year.1 That is the rate at which the Mid-Atlantic Ridge is spreading - and, coincidentally, the rate at which our hair and fingernails grow. When you get a haircut, the length of your hair that is cut equals the distance we have travelled towards Asia.
Measured in English units, one inch per year is almost a foot per decade, or nearly a yard each century. Since the Godspeed, Discovery, and Susan Constant first arrived in 1607, Jamestown has moved about 10 yards westward with continental drift. Since the first immigrants from Asia walked into Virginia (or maybe they sailed from southwestern France?) about 12,000 years ago, Virginia has drifted about the length of a football field. In the last million years, Virginia moved 15 miles to the west through continental drift.

The topography of Virginia was formed through a series of continental collisions that created vast mountain ranges in Virginia, and the ancestral Appalachian Mountains may have been 20,000 feet high.2 The collisions that created tall mountain ranges in Virginia were followed by erosion that etched away those mountains. The eroded sediments piled up in valleys and, ultimately, along the shorelines of the Atlantic Ocean and Gulf Coast.
Virginia is not as flat as a pancake today, despite 200 million years of rain and wind and gravity. Some ridges have resisted erosion, and there may be some uplift underway due to tectonic forces that squeeze the North merican Plate as it moves. To understand why there are individual ridges in some places and valleys in others, it helps to know the history of those collisions. And since the locations of towns, highways, even soccer fields is determined in part by the geology of Virginia, it helps to understand the bedrock and the topography if you want to understand the people and the culture of the state. (Could we have mountain music or "mountain dew" - moonshine whisky - without mountains?)
Not everyone is a geologist, or even a geologist wanna-be. If you find yourself slightly uncomfortable with the idea that the solid earth is not solid, then put the science into context with more-familiar terminology by reading Using Cereal Bowls and Car Crashes to Understand Virginia Geology. For the solidly-scientific perspective, see The Geology of Virginia from William and Mary, and The Geological Evolution of Virginia and the Mid-Atlantic Region from James Madison University.