From wikipedia:
Invasive species is a phrase with several definitions. The first definition expresses the phrase in terms of non-indigenous species (e.g. plants or animals) that adversely affect the habitats they invade economically, environmentally or ecologically. It has been used in this sense by government organizations as well as conservation groups such as the IUCN (International Union for Conservation of Nature).
The second definition broadens the boundaries to include both native and non-native species that heavily colonize a particular habitat.
The third definition is an expansion of the first and defines an invasive species as a widespread non-indigenous species. This last definition is arguably too broad as not all non-indigenous species necessarily have an adverse effect on their adopted environment. An example of this broader use would include the claim that the common goldfish (Carassius auratus) is invasive. Although it is common outside its range globally, it almost never appears in harmful densities.
Because of the ambiguity of its definition, the phrase invasive species is often criticized as an imprecise term within the field of ecology.