Projectile motion is concluded when a projectile stops moving. Assuming nothing gets in the way, that conclusion is reached when the projectile comes to rest on the ground.
On Earth, the motion of any projectile has both a horizontal component and a vertical component. When a projectile is fired or thrown, it is set in motion along a forward horizontal pathway. In outer space, a projectile will keep following that pathway indefinitely (at least until the influence of some other object's gravitational field causes its course to change). Near the Earth's surface, the influence of gravity begins immediately and affects the entire course of the projectile's flight. A projectile's horizontal velocity remains constant (ignoring factors such as air resistance and wind). It does not accelerate. But the force of gravity causes a projectile to accelerate in a vertical direction down toward the surface of the Earth (technically toward the center of the Earth). The influence of gravity pulls the projectile away from its straight-line original path into a curved, parabolic path. Downward acceleration continues until the projectile hits the ground and comes to rest. This state of rest where the projectile's velocity is zero in all directions is the conclusion of a projectile's motion.