What happens when a neutrino interacts with matter? Is the reason they pass through everything because matter is mostly empty space?
A neutrino interacts rarely, but when it does interact it either kicks an existing charged particle (which can be detected) or transforms a particle into another particle (for instance it can change a neutron into a proton); that particle can then be observed. The reason that neutrinos interact very little with matter is not so much because matter is mostly empty space (although that is indeed true), but rather because the intrinsic interaction of neutrinos is via the weak force only. Charged particles, in contrast, interact electromagnetically, and many other kinds of particles (e.g neutrons) can interact via the strong force. Neutrinos do not have electromagnetic or strong interactions.