A head-on collision is a collision where the directions of velocity of the two colliding bodies prior to the collision coincides with the normal direction (i.e., perpendicular direction) to the plane of contact (or tangent plane at the point of contact) of the collision. It turns out that, under these conditions, the directions of velocity of the two colliding bodies after the collision also coincide with the normal direction.
(We can actually weaken this condition to requiring only that the direction of relative velocity of the two colliding bodies prior to the collision coincides with the normal direction; the two are equivalent up to choice of inertial frame).
Head-on collisions can be viewed as collisions that can be modeled in one dimension. Collisions that are not head-on collisions are sometimes termed oblique collisions.