Dictionary
Gravitational Focusing

When talking of impacts, the concept of cross section is fundamental: in a few words, the cross section is the area occupied by the target body projected on a plane orthogonal to the direction of the motion (click here to know more about it). In fact this concept is closely tied to the probability of impact: the bigger this section is, the more probable is the impact.
In the case of an impact of a small NEO with a planet, the cross section is augmented by a phenomenon called gravitational focusing, making the probability of impact grow.

This image explains the phenomenon of focusing due to the gravitational attraction of a planet.
In the upper image the unperturbed trajectories of the asteroids are represented. In this theoretical case, the motion of the asteroids is not perturbed by the attraction of the planet and the cross section corresponds to the geometrical one.
In the lower image, the real trajectories of the asteroids are represented. It is clear that, due to the gravitational attraction of the planet, these orbits will be somehow focused by the planet. In this case the cross section is much bigger than the geometrical one.