Neutrinos come in three types, which physicists call “flavors”. The way they are made determines their initial flavor, but after they are made they can transform themselves into the other flavors as they travel. By measuring how fast they transform themselves into each of the other two flavors we can learn a lot about the neutrino, but the problem is that our conventional laboratory-made neutrino sources produce beams that are initially all of one particular flavor. We would love to have beams of the other flavors to play with, so we can learn more. We need a new type of neutrino source.
A Neutrino Factory would be a new type of neutrino source that produces an initial beam that consists of an equal mixture of two types of neutrino flavor, which is great for future experiments. Furthermore, the Neutrino Factory beam would be much better understood than a conventional beam, which would facilitate precision measurements.
The old way of making a neutrino beam is to first produce a beam of high energy charged pions and allow them to decay in a straight "decay channel", or possibly in a ring. When the pions decay they produce muons and neutrinos travelling roughly in the direction of the parent pion.
The new Neutrino Factory idea is to create a beam of low energy charged pions, allow them to decay is a straight "decay channel", capture the resulting muons, manipulate the muons to produce a very bright mono-energetic beam, accelerate the muon beam to the energy of choice, and store the muons in a ring designed to have very long straight sections. This produces an intense neutrino beam travelling in the direction of the straight sections."