They are called rare earth because their composition elements found in the "Rare Earth" or Lanthanides portion of the Periodic Table of Elements.
Neodymium magnets (Nd-Fe-B) are composed of neodymium, iron, boron and a few transition metals. Samarium cobalt magnets (SmCo) are composed of samarium, cobalt and iron. These rare earth magnets are extremely strong for their small size, metallic in appearance and found in simple shapes such as rings, blocks and discs.
