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A rare-earth element (REE) or rare-earth metal (REM), as defined by IUPAC, is one of a set of seventeen chemical elements in the periodic table, specifically the fifteen lanthanides, as well as scandium and yttrium. Scandium and yttrium are considered rare-earth elements because they tend to occur in the same ore deposits as the lanthanides and exhibit similar chemical properties. For the same set of mineralogical, chemical, physical (especially electron shell configuration), and related reasons, a broader definition of rare earth elements including the actinides is encountered in some cases. Thorium is a significant component of monazite and other important rare earth minerals, and uranium and decay products are found in others. Both series of elements begin on the periodic table in group 3 under yttrium and scandium.
Rare-earth elements are cerium (Ce), dysprosium (Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho), lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr), promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium (Tm), ytterbium (Yb), and yttrium (Y).
Despite their name, rare-earth elements are – with the exception of the radioactive promethium – relatively plentiful in Earth's crust, with cerium being the 25th most abundant element at 68 parts per million, more abundant than copper. They are not especially rare, but they tend to occur together in nature and are difficult to separate from one another. However, because of their geochemical properties, rare-earth elements are typically dispersed and not often found concentrated as rare-earth minerals in economically exploitable ore deposits. The first such mineral discovered was gadolinite, a mineral composed of cerium, yttrium, iron, silicon, and other elements. This mineral was extracted from a mine in the village of Ytterby in Sweden; four of the rare-earth elements bear names derived from this single location.

Source: Wikipedia