When an army crosses a border into another country for battle, they are making an incursion into enemy territory. An incursion is an invasion as well as an attack.

Incursion can also be used to describe other things that rush in like an army such as an invasive species into a new region or floodwaters entering your home. When an airplane heads onto a runway it is not supposed to land on, risking airport safety, it is known as a runway incursion. And an incursion of cold air could make September feel like December.

Primary Meanings of incursion

the act of entering some territory or domain (often in large numbers)
the mistake of incurring liability or blame
Full Definitions of incursion

n the act of entering some territory or domain (often in large numbers)

“the incursion of television into the American living room”
Type of:
entering, entrance, entry, incoming, ingress
the act of entering

n an attack that penetrates into enemy territory

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the action of penetrating between or among
a penetration of a barrier such as an enemy's defense
the act of invading; the act of an army that invades for conquest or plunder
a process in which individuals (or small groups) penetrate an area (especially the military penetration of enemy positions without detection)
foray, maraud, raid
a sudden short attack
air attack, air raid
an attack by armed planes on a surface target
an invasion or hostile attack
a very rapid raid
Type of:
attack, onrush, onset, onslaught
(military) an offensive against an enemy (using weapons)

n the mistake of incurring liability or blame

Type of:
error, fault, mistake
a wrong action attributable to bad judgment or ignorance or inattention

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