In theoretical physics, compactification means changing a theory with respect to one of its space-time dimensions.
For this purpose it is assumed the extra dimensions are "wrapped" up on themselves, or "curled" up on Calabi–Yau spaces, or on orbifolds.
In this way, the ten-dimensional type IIA string theory can be described as the compactification of M-theory in eleven dimensions.
The formulation of more precise versions of the meaning of compactification in this context has been promoted by discoveries such as the mysterious duality.
A flux compactification is a particular way to deal with additional dimensions required by string theory.