This tag should be used in the context of superstring theory or the geometrical shape. This tag should be used for Calibi-Yau manifolds and not other types of manifolds or Calibi-Yau algebra. Do not use this tag unless your question specifically asks about Calibi-Yau manifolds - this tag should not be added just because your question is about superstring theory.
Below is an example of a Calibi-Yau manifold.
Calibi-Yau manifolds are a special type of manifold that can be described in certain branches of mathematics, such as algebraic geometry. The properties of Calibi-Yau manifolds lead to their application in theoretical physics, especially superstring theory. They are shapes that satisfy the requirement of compactification for the six "hidden" dimensions of superstring theory.