Standard solar model
Physicists use the term Standard Solar Model (SSM) to describe the best current physical model our sun. Very generally, in the Standard Solar Model the sun is a ball of mostly hydrogen plasma which is held together through self gravitation. At the core of the sun the temperature and density are large enough that hydrogen atoms may be converted to helium through several different processes. The conversion of hydrogen to helium releases a large amount of energy, and also results in the production of two electrons and electron neutrinos. The energy continually produced in the core keeps the sun in equilibrium, neither exploding nor collapsing further. As the ratio of hydrogen to helium in the core changes the core temperature and density also change, and this affects the size and luminosity of the sun. Like the Standard Model of particle physics and the standard cosmology the SSM changes over time in response to relevant new theoretical or experiment discoveries.
Neutrino production
Hydrogen is fused into helium through several different interactions in the sun. The vast majority of neutrinos are produced through the pp chain, a process in which two protons collide to produce a proton, neutron, electron, and electron neutrino. These "pp neutrinos" are by far the most common ones produced in the sun, but their energy is so low (<0.425MeV) that they are very difficult to detect.
Neutrino detection
The weakness of the neutrino's coupling with other particles means that most neutrinos produced in the core of the sun can pass all the way through the sun without being absorbed. It is possible, therefore, to observe the core of the sun directly by detecting these neutrinos. The first experiment to successfully detect solar neutrinos was Ray Davis's chlorine experiment, in which neutrinos were detected by observing the conversion of chlorine nuclei to argon in a large tank of perchloroethylene. The experiment found about 1/3 as many neutrinos as were predicted by the Standard Solar Model of the time, and this problem became known as the solar neutrino problem.
While it is now known that the chlorine experiment detected neutrinos some physicists at the time were suspicious of the experiment, mainly because they didn't trust such radiochemical techniques. Unambiguous detection of solar neutrinos was provided by the Kamiokande-II experiment, a water Cerenkov detector with a low enough energy threshold to detect neutrinos through neutrino-electron elastic scattering. In the elastic scattering interaction the electrons strongly point in the direction that the neutrino was travelling, away from the sun. This ability to "point back" at the sun was the first conclusive evidence that the sun is powered by nuclear interactions in the core. While the neutrinos observed in Kamiokande-II were clearly for the sun the rate of neutrino interactions was again supressed. Even worse, the Kamiokande-II experiment measured about 1/2 the predicted flux, rather than the chlorine experiment's 1/3.
The solution to the solar neutrino problem was finally experimentally determined by the Sudbury Neutrino Observatory. The radiochemical experiments were only sensitive to electron neutrinos, and the signal in the water cerenkov experiments was dominated by the electron neutrino signal. The SNO experiment had sensitivity to all three neutrino flavours, and by simultaneously measuring the electron neutrino and total neutrino fluxes the experiment demonstrated that the suppression was due to the MSW effect, the conversion of electron neutrinos from their pure flavour state into the second neutrino mass eigenstate as they passed through the changing density of the sun.