A manifold is said to be orientable if it can be given an orientation. Note the distinction between an "orientable manifold" and an "oriented manifold," where the former implies the possibility of giving the manifold in question an orientation, while the latter implies that the manifold has already been given an orientation.
See alsoManifold, Manifold Orientation
This entry contributed by Rasmus Hedegaard
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Hedegaard, Rasmus. "Orientable Manifold." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/OrientableManifold.html