Defining an invasive species can be difficult, as there are varying opinions, however in general:
they have a negative impact on environmental, economic or public priorities
most are non-native or not naturally found in the ecosystem, however, not all are non-native
most have a high capacity to reproduce and distribute within it's new environment
Sometimes a species is invasive in one part of the country, but not another. Other species are often called "conflict" species.
Feral Swine - an invasive species. Feral swine were introduced in the United States from Eurasia and North Africa. Escaped and became feral, expansion probably aided by drainage of land. Highly destructive to native habitats, agricultural communities and increase risk of disease to livestock and humans.
White Tailed Deer - a native species to the U.S. However, some populations (e.g. northeastern U.S.) have increased dramatically and cause problems by consuming plants valued by humans in farms, yards, and native habitats. However, most people would not consider them an invasive species.
Coyote - native to the midwest, however over the last 150 years they have expanded their range to almost the entire continental US. Extending north to Canada and Alaska and south to Central America. They are considered "conflict" species because they prey upon livestock and in some areas considered invasive due to reported negative impacts on wildlife and game species.