Neutrinos are like electrons except they have no electric charge. They are the most prolific type of matter-particle in the Universe. In fact, neutrinos outnumber the ordinary stuff we are made of (electrons, protons, neutrons) by a factor of 10 billion. Yet we don’t know all of their properties, and the properties that we do know, we don’t understand. For example, they weigh almost nothing. In fact they are a million times lighter than electrons, but we don’t know why. They also come in three types, again we don’t know why. It might be that their properties are responsible for the early Universe ending up with matter in it and essentially no antimatter, rather than an equal mixture of both matter and antimatter which then annihilate, leaving no stuff from which to make us. If this is the case then the mysterious neutrino makes it possible for us to exist.
One reason why we know so little about neutrinos is because they don’t interact very much. You need to make vast numbers of them in order to do experiments, and you need super massive detectors to make enough of them interact so that they can be detected and measured.
The goals for a Neutrino Factory is to make enough neutrinos of the right type in a controlled way so that new experiments can teach us more about this mysterious particle, and reveal its properties and its role in the Universe.