Native species are those that "belong" here. In normal use, that means the species were in Virginia before the arrival of the Europeans. Sailors from various nations visited the coastline of Virginia in the 1500's, and the Spanish landed a party in 1570, but the settlement of Jamestown in 1607 is often considered the reference point for "native" and "non-native" species.
It helps to remember that the Native Americans imported crops into what became Virginia - corn, beans, and squash in particular - before the Europeans arrived.
The balance of nature in the state of Virginia has been tilted by non-native species. Some were brought here; cows, horses, honeybees, pigs, potatoes, and most other agriculturally-valuable species are not native to Virginia. Even the species of tobacco that we grow is not native.
Other species hitchhiked here uninvited, including Japanese honeysuckle and the veined rapa whelk. Aquatic organisms are hard to see unless you're a waterman, but can involve great expense. The zebra mussel is here, and companies with intake pipes drawing water from the freshwater rivers fear they may have to spend heavily to keep their intake/discharge pipes clear of obstruction.
Some of our most common plants and animals are not native. That "English sparrow" pecking away at the crumbs outside McDonalds, the starlings feeding in a flock at the edge of an open field, the Japanese honeysuckle vine climbing along the fenceline - none of them are native to Virginia. They are aliens, imports from outside the state.
Does that make them lesser species? Not necessarily. The Clematis growing wild at Aquia Landing park in Stafford County smells wonderful - but it's a non-native species. The native version is an equally-pretty climbing vine with a white flower, but it lacks the perfume of the non-native species. The hydrilla that is expanding along the bed of the Potomac may clog the channels into marinas. Still, it's clearly serving the function of submerged aquatic vegetation, trapping silt and providing a place for invertebrates to grow.
Some non-natives are harmful, however. Purple loosestrife and Phragmites spread throughout Virginia wetlands, displacing native species that the animals have used as food sources. The non-native species, while large and "showy," do not provide the same food value to the animals in the area. The native critters are unfamiliar with the non-native plants, and do not utilize their biomass effectively. Plants and animals that have evolved together create a web of life which adapts gradually to change. As a result, the exotics - in these two cases, invasive species that spread rapidly - reduce the health of the native animals in the wetlands.
Other non-native species in Virginia include carp, coyotes, feral pigs at Back Bay National Wildlife Refuge, mute swans in the Chesapeake Bay, nutria, and Sitka deer at Assateague Island.
Kudzu is now a classic image of the South, since it's common on roadsides down here but rare in the colder areas north of Virginia. [Anyone seen it on the roadcuts for the Pennsylvania Turnpike?] It was used to revegetate areas where the soil was disturbed by construction, under the theory that green things holding the soil against August thunderstorms are good things.
Kudzu became popular with the highway departments because it grows very fast in poor soil. In a roadcut, bare red clay baking in the summer sun is a tough place to grow. Invasive species are typically able to get a competitive advantage in such disturbed sites - 'cause the native species have evolved to thrive in the normal habitats.
Kudzu is really common in Virginia south of the James, and on Highway 60/I-64 east of Richmond. One reason it does so well is because kudzu manufactures its own fertilizer, as do other members of the pea family like clover and alfalfa. (Virginia farmers will use alfalfa as a hay crop, and occasionally will just plow it under as "green fertilizer" rather than feed it to horses or cattle. Hey, cheaper than going to Southern States to buy fertilizer...)
But kudzu is a killer. It will grow overtop of a pine forest, covering the canopy with a layer of vines that capture all the sunlight at the top. That shades out the trees, and everything underneath dies. Then in the cold winters, the vines will freeze and the hillside will be a barren tangle of rotting trees and withered vines. The next spring, the vine-that-can-eat-a-forest will come back (the roots don't freeze below the frost line, in the 56-degree ground...) and cover the surface with big green leaves again.
And kudzu is not a producer of nuts or fruits, or even leaves that are attractive to Virginia's wildlife. Think about it - our critters have evolved to feed on native plants, and are not normally adapted to take advantage of invasive species. When you were young, did you like bitter foods such as coffee? Our wildlife suffers when an oak-hickory forest is converted into a kudzu-covered field. You won't normally find deer peacefully browsing the kudzu branches, or wood thrushes nesting in its branches...
The kudzu profile: