In the context of analytic geometry, a polydisc is a product of discs: the analytic space which is formally dual to the Tate algebra T n (for an n-dimensional polydisk).
This is a basic analytic space. It is the analog in analytic geometry of the affine space 𝔸 n in algebraic geometry.
Every complex analytic manifold is locally isomorphic to a polydisk.
Those analytic spaces which are subspaces of polydiscs are called affinoids.