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Another word for a 
(infinitely differentiable) Manifold. A smooth manifold is a Topological Manifold
together with its ``functional structure'' (Bredon 1995) and so differs from a Topological Manifold because the notion
of differentiability exists on it. Every smooth manifold is a Topological Manifold, but not necessarily vice versa.
(The first nonsmooth Topological Manifold occurs in 4-D.) In 1959, Milnor showed that a 7-D Hypersphere can be
made into a smooth manifold in 28 ways.
See also Differentiable Manifold, Hypersphere, Manifold, Topological Manifold
References
Bredon, G. E. Topology & Geometry. New York: Springer-Verlag, p. 69, 1995.