Deuterium and tritium are two isotopes of hydrogen.  Whereas the nucleus of ordinary hydrogen is just a proton, deuterium (D) has a proton and a neutron, and tritium (T) has two a proton and two neutrons.

Of all the possible combinations of nuclei colliding the probability of a fusion reaction occurring is highest for D-T.  This probability is usually called the fusion reaction cross section.

If the nuclei are moving fast enough they can get close enough together to overcome the repulsion from the positively charged protons, and fuse.  This binding of the nucleons (protons & neutrons) allows them to rearrange into a helium-4 nucleus (often called an alpha particle) and a free neutron.  Releasing a huge amount of energy from the difference in mass of the D-T before and the He-4 and neutron after, according to the famous E=mc^2 equation.

The reaction can then be written as:

D + T ->  He-4 + n + 17.6MeV

The energy is released in the form of kinetic energy of the particles, and due to the conservation of momentum this is divided up with the He-4 getting 3.5MeV and the neutron getting 14.1MeV. Since the neutron is roughly 4 times lighter than the He-4.

Since it can occur at lower temperatures than other fusion reactions it is currently the leading candidate for mainstream fusion projects such as ITER and NIF.