Neutrinos were long believed to be massless particles which always travel at the speed of light, just like photons. They exhibit a sort of chirality in the sense of their quantum mechanical spin. While particles that have mass can spin in a right-handed or left-handed sense around their direction of motion, neutrinos can only spin in a left-handed sense (and antineutrinos in a right-handed sense). Such an intrinsic chirality is impossible for particles with mass, because the direction of spin of the latter can be changed by rotating the particle in its rest frame. This is why neutrinos were thought to be massless.

Let us now introduce the lepton number, which is #leptons – #antileptons. It is known from the Standard Model that the lepton number is always conserved. However according to GUTs, the lepton number may vary slightly by the effects of grand unification. If the lepton number is not conserved, then the neutrino and the anitneutrino could be two states of one particle. So neutrinos could have mass, but it would have to be very small since it arises from the effects of the GUT. There are three types of neutrinos: electron neutrino, muon neutrino and tau neutrino. If the neutrino does have mass, then while travelling through the vacuum, one type of neutrino can convert spontaneously into another. This is known as neutrino oscillation.

By studying neutrinos emitted by the Sun or created by cosmic rays in our atmosphere, physicists learned that neutrinos actually have a tiny mass. These studies showed evidence for neutrino oscillation. If this is indeed so, then the discrepancy between the number of neutrinos expected from the Sun and the number detected is resolved. Moreover, studies of the decay of the tritium nucleus have demostrated that one type of neutrino is lighter than about 2eV.

Read more:
Neutrino in Wikipedia
The Super-Kamiokande detector
Neutrino mass discovered -- Physicsworld