A neutrino is an elementary particle. This means that it can't be broken into smaller particles, as far as we know. It is electrically neutral and is affected only by the weak force and gravity. It has half-integer spin, small, but non-zero mass and it comes in three varieties, or "flavours" – electron neutrino, muon neutrino and tau neutrino. They can ocillate, or flip, between different flavours as they travel through space. Neutrinos are the second most abundant particles in the Universe, after photons. Although they have very tiny mass, because of their number they make a significant portion of the Universe's mass. They are possibly a Majorana particle, meaning that the neutrino is identical to its anti-particle, antineutrino.
Neutrinos are very hard to detect because they are tiny and travel through most of the matter at the speed near the speed of light. We can detect them when they create an electron or muon in the detecting medium, such as water or heavy water or when there is germanium or argon in detectors that use gallium or chlorine. These detectors are basically large tanks in which the medium is contained. They have to be verly large to detect significant amount of neutrinos, because neutrinos rarely interact with matter. These detectors also have to be underground to shield the medium from cosmic rays and background radiation, which are stopped by the surrounding rocks.
There are plenty sources of neutrinos in the Universe. The Big Bang is one. Stars, including of course our Sun, is another. Further, nuclear reactors, nuclear bombs, radioactive decay of some elements in Earth's rocks, supernovae and cosmic rays hitting the atmosphere all produce neutrinos. As an astronomy branch, neutrino astronomy is relatively young, but has potential to give us a different look at what goes on inside a star or during a supernova.
Neutrino has been suggested by Wolfgang Pauli in 1930 in order to explain how energy, momentum and spin are conserved during beta decay. In 1934, Enrico Fermi developed the theory of weak interaction and named the particle neutrino. It has been experimentally discovered in 1956 (actually it was anti-neutrino that was discovered then, originating in a nuclear reactor). Sun-made neutrinos were detected in 1968. Since then, neutrino astronomy has been gradually developing and now offers us a new way to look at the Universe.