An invasion is the movement of an army into a region, usually in a hostile attack that's part of a war or conflict. World history is full of descriptions of invasions.
One country's army plundering or taking over a city or piece of land in another country is an invasion. You can call other mass movements invasions as well, like a horrifying invasion of your kitchen by cockroaches, or the invasion of a stadium by excited soccer fans. A common phrase is "invasion of privacy," which means an unfair intrusion into someone's personal space or private information.