It's invasive when it's introduced by humans and outcompetes the native inhabitants. Which disrupts naturally occurring ecosystems.

Kudzu is an example. It's native to Asia, but it's a fast growing vine that does very well in the climate where I live. I was told it was originally brought over to help keep soil in place after construction work. Issue is that it's wild now, and it outcompetes basically everything else so you end up with huge swaths of just kudzu. It's a creeping vine that will literally cover a football field of forest, and strangle every tree there to death. Which ruins that habitat for fauna- squirrels can't navigate it properly, birds don't have trees to nest in anymore, etc.

So, yeah, the concept of an invasive species is entirely human made because it's a thing caused by humans.

Basically, it's usually considered invasive when it is brought to a new place by humans, and then takes entirely too well to the new place- usually because it doesn't have any natural predators to keep it in check.