Radioactive decay is when the nucleus of an atom isn't stable - it could have too many protons that push each other apart, or too many neutrons, and it's just like a big lump of rock and can fall apart.
There are three kinds of radioactive decay, all named after Greek letters: alpha (#alpha#), beta (#beta#) and gamma (#gamma#).
#alpha#-decay happens in unstable nuclei and an #alpha#-particle is emitted, which is equivalent to the helium nucleus. Two protons and two neutrons are emitted, reducing the total mass number by four and the atomic number by two, making the atom into a new, smaller, more stable element.
#beta#-decay is when you've got too many neutrons, so a neutron decays into a proton. In order to conserve charge, an electron is released, and an anti-neutrino, but that has no charge or mass. You can also have #beta#-decay of a proton into a neutron, where a positron (antimatter electron) is emitted.
#gamma#-decay is where the atom emits a photon with the wavelength of a #gamma#-ray, hence the name. This kind of radioactivity is the most damaging because of the high energy and penetration of the #gamma#-ray.