Design Nomenclature / Form & Geometry
Local space
Also called object space, pivot, origin, local coordinates
The coordinate frame an object's vertices are actually stored in: origin at the object's pivot, axes fixed to the object. Vertex data does not change when the object moves — the transform matrix does. Each child in a hierarchy is stored in its parent's local space, and that nesting is what makes rigs composable at all.
In practice
'Object space', and the pivot is simply its origin. A pivot left at the world centre is why rotating a part swings it across the scene instead of turning it in place; 'centre pivot' moves the frame, not the mesh.