Cross section does not describe the actual physical size of a target particle. Instead, it describes how likely an interaction is for a given number of incoming particles. A larger cross section means a higher chance that an incoming particle will interact with the target.
Scientists define cross section so that the reaction rate equals three things multiplied together. These are the incoming particle flux, the number of target particles per unit volume, and the cross section itself. This links a tiny, microscopic property to reaction rates that can actually be measured in the lab.
Cross sections are not fixed numbers. They change a great deal depending on the energy of the incoming particles. They also depend on which specific process is being studied, such as elastic scattering, absorption, or ionization.
Because of this, a single target material can have many different cross sections. Each one applies to a specific type of interaction and a specific particle energy. Nuclear engineers rely on measured cross sections to predict how a reactor core will behave under different conditions.
Very small cross sections often require intense particle beams or long exposure times to gather enough data. The term cross section is a little misleading. Particles usually behave more like waves than solid spheres in these interactions.