Naturalized plants are plants established as a part of the flora of a locale other than their place of origin. When a plant naturalizes in an area, this can be either a "good" or a "bad" thing, depending on your opinion of the particular naturalized plant.
For instance, when we buy exotic bulb plants that have pretty flowers and plant them in our gardens, we're delighted if the plants become naturalized plants. Sometimes, however, exotic, or "alien" plants that become naturalized plants later come to be looked upon as nuisances. Tenacious enough to spread without humankind's help -- and perhaps even in spite of our attempts to eradicate them -- such naturalized plants tend to acquire a pejorative designation: namely, "invasive." The naturalized plants in such cases can end up crowding out indigenous plants.
An example of such a plant in North America and the U.K. is Japanese knotweed, a naturalized plant from Asia.