The chemical elements that make up the Rare Earth Minerals collectively contain Lanthanides as well as Scandium and Yttrium. These elements share similar chemical characteristics.
The rare earth elements are not particularly uncommon in the sense that they have been defined in terms of their general availability and abundance in the Earth's crust.
The Earth's crust contains plenty of rare earth, but they are classified as rare because they are present in extremely small amounts and because their dispersed nature makes it extremely difficult and expensive to locate, extract, and process them.