The overall goal of the CCFR collaboration was to look at the results from neutrino-nucleon deep-inelastic scattering (or "DIS"). What does this mean? Let's break the phrase down into its individual words:
At the relativistic energies of modern particle physics, the kinetic energy and momentum of most particles are almost the same, so for our purposes we have different definition: In an elastic collision, the beam and target particles are unchanged after scattering; in inelastic scattering, the beam and/or target particles are fragmented by the scattering. At the energies of this experiment, the target particle (e.g., a proton) is fragmented and transformed into many other particles, and so the interaction is called "deep" inelastic scattering.
The target in this experiment is made mostly of iron. The most massive part of an iron atom is its nucleus, which is composed in turn of "nucleons" -- protons and neutrons. It is the protons and neutrons that are considered to be the target of the beam, and hence it is referred to as "neutrino-nucleon" scattering.
Another term for protons and neutrons is baryons (it's a matter of context: they're called nucleons when they're inside an atomic nucleus, and baryons when they're considered as a class of particles). Baryons are made out of quarks. The flavor of quarks inside a baryon determine what its type; a proton is made of two "up" quarks and two "down" quarks, while a neutron is made of two "down" quarks one "up" quark. The force that holds the quarks together is the strong nuclear force.
One of the goals of the CCFR experiment is to understand proton structure. We can do this because, while the neutrino is inelastically scattering off the nucleon, it elastically scatters off of the quarks inside the nucleon. To get some insight how this works, we must look more closely at deep-inelastic neutrino scattering.