T2K is a second generation neutrino oscillation experiment. It uses an off-axis neutrino beam that is produced at J-PARC accelerator complex in Tokai at the east cost of Japan. The accelerator complex will eventually produce the world most intense long baseline neutrino beam by dumping protons at a beam power of around 500 kW onto a carbon target. The resulting neutrinos are first measured by a near detector complex before they continue 295 km to the Super-Kamiokande detector.
At the sub-atomic level, matter - the stuff we are made of - is made from up-quarks, down-quarks (which together form protons and neutrons) and electrons. A fourth member of this group, the electron-neutrino is not part of the atoms we are made of, it is electrically neutral and is not able to stick on to the other components of matter, and so it is not as famous as the others. Indeed, it interacts so weakly with normal everyday matter that a neutrino can easilly pass all the way through the Earth without interacting. Neutrinos are produced naturally in radioactive beta-decay, in the fusion processes which make the sun burn and we can make beams of them from particle accelerators.
For reasons we don't yet know, nature has chosen to not only have these four particles (the up-quark, down-quark, electron and electron neuttrino) but to make two copies of these particles (the charm-quark, strange quark, muon and muon neutrino) and (the top-quark, bottom-quark, tau and tau-neutrino).
It turns out that when we describe a neutrino as a quantum mechanical wave, it has to be described in terms of three component waves which each travel at different velocities. This means that as it travels, some of the crests and troughs of the three waves start to lag behind as it moves along. This makes the properties of the neutrino change as it moves. This effect is called neutrino oscillation, because if the neutrino goes far enough, it is possible for the lag of a wave crest to be so big that it lines up with the next crest of the other waves (and so we are back where we started and have an electron neutrino again). In fact, two distinct ways in which it can oscillate have already been observed: (1) muon-neutrinos from cosmic rays and from accelerator experiments change into tau-neutrinos and (2) electron neutrinos from the sun and from reactor experiments have been seen to change into the other two types of neutrino. The neutrinos have to travel about 25 times further for (2) to happen than for (1) to happen.
With three types of neutrino, there is a third combination of oscillation which is theoretically possible, but has not been seen yet. This is what we seek to measure in the T2K experiment. The way to observe it is to start with muon neutrinos (the easiest to make in an accelerator beam), let the neutrinos travel as far as needed for (1) from above to happen and then look for appearance of electron neutrinos (in (1), they only change to tau-neutrinos).