The nucleus of an atom is the site of two of the most powerful forces in nature, and they are acting in opposition. The protons of the atom all have a positive charge, and they are being pushed apart by electromagnetic repulsion. Nuclear binding energy opposes this, holding the nucleus together. Because of the delicate balance between these forces, there are some configurations of the nucleus that are unstable, and they undergo various forms of modification to achieve stability.
In some cases a particle consisting of two protons and two neutrons is ejected from the atom. This is called an alpha particle, and the emission is referred to as alpha radiation.
In beta radiation, the reorganization of the nucleus is a little different. In this case a neutron is split, creating an electron (which is released and is called a beta particle) and a proton (which remains in the nucleus).
Gamma radiation is not comprised of particles, it consists solely of high-energy electromagnetic waves. The emission of this energy allows the nucleus to settle into a more stable configuration without emitting any particles.
The main danger that radiation presents to us is the potential for damage to our cells, and especially to our DNA. Although alpha particles are fairly low speed and consequently easily stopped, the higher energies of beta and gamma radiation allow them to penetrate into our cells and do damage on the way by. Imagine being shot by a number of very tiny bullets, and that will give you some idea of what radiation does to the body.
Radioactivity - or the particles or energy called radioactivity - comes from the nucleus of an atom. Radioactivity is the spontaneous release of energy and/or particles from the unstable nucleus of an atom. A nucleus is unstable because of its number of protons and neutrons. That explains why some isotopes of an element are radioactive while others are not. When the unstable nucleus releases decay energy and/or particles it results in a more stable nucleus.