Some nuclei are unstable. This is often because they have too many neutrons or are too large. An unstable nucleus becomes more stable by giving out radiation. This process is called radioactive decay and a nucleus that does it is radioactive.
An unstable nucleus can emit four types of radiation. An alpha particle is made of two protons and two neutrons, so it is the same as a helium nucleus. A beta particle is a fast moving electron that comes from the nucleus, not from the electrons outside it. A nucleus can also emit a single neutron.
Gamma rays are different because they are electromagnetic radiation, not particles. They have no mass and no charge. The decay of any one nucleus is random, which means it cannot be predicted when it will happen.