Neutrinos are a type of fermion which has no charge and is extremely light, so much so that most physicists believed it had no mass until quite recently. The thing about neutrinos is that they barely interact with anything: billions go through you every minute without you even noticing.
The story of how we found out about neutrinos is great for showing how discoveries are made in science. It all started by looking at a particular type of radioactive decay called beta decay, in which a nucleus gives off an electron.
Scientists were expecting to see electrons that were always shot with the same energy, as they had seen in many other decay processes. However, they found that the electrons had a range of energies. Some energy was missing. From there, somebody guessed that the energy had to be carried by another particle, since it couldn’t have just vanished. The particle couldn’t have any charge, because otherwise the total charge would not add up. And it had to be very light because, if it weren’t, it would have to carry a huge chunk of the energy, but there were times when the electron had almost all of it. So we have a small, neutral particle: the neutrino.
This chain of reasoning may seem like a bunch of patches on top of patches. Our theory does not predict the right outcome? Add a particle! Wait, but then how does the electron take most of the energy sometimes? It must be light! And why haven’t we seen it yet? It has no charge! However, this is how science works: we look for a plausible explanation, which we refine using the data at our disposal. We make new predictions and see if they fit. If not, we throw the new idea away. In some cases, our idea survives and we have a new theory or a new particle, in this case the neutrino.
To be precise, the neutrinos from the beta decay are actually antineutrinos: particles which, when set in contact with a neutrino, will annihilate into photons. However, since the neutrinos have no charge, it is almost identical to its anti-particle.