Particle physicists often use the word "cross-section", but what does it mean? Put simply, the cross-section gives you an idea of how often a particle will interact with the particles in your detector.
In a classical analogy, where a particle is modelled as a hard sphere, the cross section is the conventional geometric cross sectional area, and expresses the probability of hitting the object with a ray. Physicists denote it with the greek letter “sigma” and measure it in units of area. In the world of point-like particles, the cross-section "area" is determined by the particles' ability and likelihood to interact with others.
Since neutrinos only interact via the weak force (they have no electric or colour charge), the neutrino cross-section is very very very very small. This implies that the probably of witnessing an interaction induced by a neutrino is very very very very small. Unfortunately the only way to study neutrinos is to detect them, making physicists' lives very hard! The particles are so elusive that one light-year of lead (which equals nine and a half trillion kilometres, or six trillion miles) would only stop half of the neutrinos flying through! That is why scientists need to produce a very intense neutrino beam to find at least some that interact in the detector.