Invasive means "tending to spread very quickly and undesirably or harmfully".
As wikipedia says "An invasive species is an organism that causes ecological or economic harm in a new environment where it is not native. ... Invasive species are capable of causing extinctions of native plants and animals, reducing biodiversity, competing with native organisms for limited resources, and altering habitats".
But the term "invasive" it's not always so simple to define and can be quite subjective.
In Hong Kong we have some really bad and invasive species, like the red-eared sliders; the Apple snail; the Red Imported Fire Ant; and the House Crow. We have to add to this the plants Sonneratia and Mikania micrantha (an exotic perennial herbaceous vine, aka the "mile-a-minute" weed). These are all recognised as posing a threat to the local ecology by the government, so we need to look out for them.
The red-eared slider; so cute and cheap when young, but a real problem in our parks and ponds.
Some introduced animals and species are not so bad. Although a detailed database on invasive alien species is currently not available, the Government has recorded information related to alien species; for instance, Hong Kong currently has over 3,000 plant species, among which about one-third are alien species, including some common fruit trees and ornamental plants. A large number of introduced species have long been naturalised in Hong Kong, and have no significant impact on the local ecology. Many of the weeds in cultivated areas are exotics, as are the fish in the concrete channels that you see in the towns in the New Territories, many the result of the buddhist release programmes that are so harmful. Oh, and lets not forget the "American" cockroach and the Giant African land snail...and the greenhouse frog (Eleutherodactylus planirostris) which I often find on my walks, but these are not so damaging. Much like the chinese/green water dragons, which have established breeding colonies but do not really threaten any local species.
Beware invasive species....
There have so far been two alien disasters in Hong Kong: the Pinewood Nematode (from North America) and Pine-needle Scale Insect (from Taiwan), which together virtually eliminated the native Pinus massoniana in the 1970s and 80s. The chance of another disaster increases every time an additional alien species becomes established in Hong Kong. So we do need to be mindful.
Also some species are introduced to help with a problem, but they can often end up also being a problem. Like the macaques. While monkeys were once indigenous to the city they were probably wiped out by habitat loss and hunting, so the macaques of Monkey Hill were re-introduced to help solve the poisonous plants problem around the reservoirs, and now their population is growing.
In low-lying wetlands and rivers, mosquitofish – initially imported to eat mosquito larvae – and the tilapia fish – are classified by the International Union for Conservation of Nature as one of the world’s worst alien invasive species. .....they have been replacing native species such as the ricefish in streams. So a government policy also going wrong.
My personal nightmare are the red-eared sliders - as they decimate other pond life - and the "mile a minute" weed that covers much of our woodland and forest.