Linked from
The 8 pages that link to Support function, each with the reason it gives.
Convex setRelated: It encodes a closed convex set through its supporting directions.
Convex bodyRelated: It records the furthest extent of a convex body along every direction.
Barbier's theoremRelated: The difference of opposite support values encodes each directional width.
Bipolar theoremRelated: Polar inequalities can be expressed through bounds on linear functionals.