and
Supergeometry is the (higher) geometry over the base topos on superpoints modeled on the canonical line object in there.
As ordinary differential geometry studies spaces – smooth manifolds – that locally look like vector spaces, supergeometry studies spaces – supermanifolds – that locally look like super vector spaces.
As ordinary algebraic geometry studies spaces – schemes – that locally look like affine spaces, supergeometry studies superscheme?s.
From the point of view of noncommutative geometry, the supergeometry is a very mild special case of noncommutativity in geometry: some coordinates commute, some anticommute.