A use of the term cross section in the physics of particles moving close to each other is a representation of the probability of interaction between the particles as if it were an area around one of the particles. Among the areas of physics where the concept is used is nuclear physics (fission and fusion, such as the power generation within stars), in radiative transfer, and in the physics of gases as interacting particles (kinetic theory of gases). The term collision cross section is sometimes used when the interactions are thought of as collisions between particles.
In the mechanics of small particles (quantum mechanics), particles passing at a certain distance of each other may or may not interact, an interaction having some probability whose calculation is the business of quantum mechanics. If a specific region were selected around one particle that includes nearly all points at which another passing particle might interact (so the probability of interacting with a particle passing outside this region is virtually zero), then the cross section is a smaller region sized so the ratio of region sizes matches the probability of an interaction of a particle passing through the larger region. It is a convenient and simplifying method of modeling how many interactions will take place.
Given such a cross section, the path of a moving particle can be viewed as a straight, round, tube-shaped volume, whose calculated volume along with the density of the material allows calculation of properties of interest such as how long the particle is likely to move before an interaction (the mean free path).
Cross sections are used in quantifying scattering effects such as Compton scattering. For scattering, the differential cross section is the ratio between the area-size of the cross section and the solid-angle size of the possible directions to which something can be scattered. It is a function of the scattering angle. In some kinds of experiments it can be worked out through scattering statistics and serves as a step toward calculating the cross section.