Neutrinos are fundamental particles, like electrons. That is, they cannot be divided up any further. This distinguishes them from the protons and neutrons found in atomic nuclei, which are each composed of three quarks (yet another kind of fundamental particle).
Neutrinos have no electric charge, which means that unlike electrons, they cannot be affected by electric or magnetic fields. Nor can they (directly) produce photons (quantum packets of light). Also, unlike the family of quarks, they cannot interact via the strong nuclear force. So unlike electrons and quarks, they are not bound up in atoms, and they can be seen only via the aptly named weak interaction. This makes them awfully hard to detect! They are often referred to as "ghost particles." Indeed, neutrinos were first hypothesized in 1930 by Wolfgang Pauli, but not detected experimentally until 1956.
Because neutrinos interact so little with the matter we humans consider normal, they provide a great way to see inside objects whose interiors are otherwise difficult to observe. For instance, neutrinos have already been detected from the center of the Sun, from the 1987 supernova in the Large Magellanic Cloud, and from deep within the crust of the Earth. It has even been proposed to use a neutrino detector to discover unauthorized reactors manufacturing fuel for nuclear bombs, although this idea currently seems a little far-fetched.
The electron and neutrino are part of a family of fundamental particles called leptons. It is an observed, but so far unexplained, fact that there are two types of particle in the lepton family, the "muon" and "tau," that are exactly like the electron, but heavier. In fact, neutrinos also come in three types, each one associated with a corresponding charged lepton (electron, muon or tau). But we do not yet know how the masses of the different neutrinos compare, only that they are no more than a millionth that of the next-lightest particle with mass, the electron.
To continue reading about neutrinos, you can learn how we know they have mass.