Howie, an invasive plant is one which has the ability to outcompete native plants and especially, whole plant communities. It's not about how "aggressive" a given plant is, although that could be a part of the picture. Ecological invasion is where the plants
(and other organisms that need those plants) which are adapted to a given area are crowded out by species which are better able to cope with the disturbances which are constantly being placed on the landscape, many of which are coming from things we humans are doing.

I'm seeing where lots of peoploe are thinking an invasive plant species is just something that grows fast or grows into another plant's area. IT's much more than that. The worst offenders tend to be plants with fruits which birds then eat, pooping out the seeds for miles around. This is the exact mechanism whereby nearly every woodlot or forest in my part of the state of Wisconsin has been overrun by common buckthorn, a Eurasian species which has numerous weapons at its disposal; Highly shade-tolerant, it can come up in the shadiest of spots and can grow in the shade that it itself produces. Allelopathic, this plant exudes chemicals from its root tips which tend to hold back other plant types from growing there. Able to use more of the growing season than most native species-it's up and running earlier in the spring and later in the fall (both factoids of which can be used to our advantage in controlling this plant. But I digress.