Something is invasive is encroaching or trespassing, invading or attacking (as in diseases), or, in medicine, enters the body via puncture or incision.
Invasive species are plants or animals introduced into an environment that steadily spread throughout that environment, sometimes taking over, because they have no natural predators to keep their growth in check. The same could be said of diseases such as cancer. Invasive surgery usually involves making an incision with a scalpel. We call policies or laws invasive when they endanger personal or civil rights and liberties.