Alpha/beta particles and gamma rays are the three most common forms of radiation emitted by unstable or radioactive isotopes. All three were named by a New Zealand-born physicist named Ernest Rutherford in the early part of the 20th century. All three kinds of radioactivity are potentially dangerous to human health, although different considerations apply in each case.
Protons in a nucleus are positively-charged particles, so they repel each other. The force that overcomes that repulsion and holds them together is called the strong force or strong nuclear force -- a force that acts between neutrons and protons in a nucleus, but only at very short range. If the nucleus has too high or too low a ratio of neutrons to protons, it will typically be unstable and hence radioactive.
An alpha particle is just a helium nucleus without any electrons -- two protons and two neutrons. It has a much greater mass than beta particles, and consequently a much shorter range. Ordinarily, it travels at about a tenth of the speed of light. When a nucleus ejects an alpha particle, its atomic number decreases by 2 and its mass decreases by 4, so it is now a different element. A sheet of tissue paper or the surface layer of your skin is sufficient to stop an alpha particle, so they have relatively little penetrating power. They are more dangerous if the material emitting alpha particles has been introduced into the human body, in which case they become extremely dangerous.
A beta particle is an electron. When a nucleus emits a beta particle, one of its neutrons changes into a proton, so the atomic number increases by 1 and it is now a different element. Beta particles travel at about 90 percent of the speed of light and have a hundred times more penetrating power than alpha particles; a sheet of aluminum will stop them however, and they only penetrate about a centimeter into human flesh.
Gamma rays are a high-frequency form of electromagnetic radiation, so they travel at the speed of light. Emission of gamma rays often follows emission of alpha or beta particles; when a nucleus ejects an alpha or beta particle, it is left in an excited or higher-energy state, and it can fall to a lower energy state by releasing a gamma ray photon. Gamma rays have much higher penetrating power than alpha or beta particles -- so much so, in fact, that they can penetrate through buildings or bodies. Thick concrete or lead shields are usually needed to ensure complete protection. The high-frequency gamma rays have sufficient energy to ionize molecules in your body, which can cause damage to important macromolecules like DNA inside your cells.