Linked from
The 20 pages that link to Affine space, each with the reason it gives.
Euclidean spaceNarrower topic: It supplies points and displacement vectors before a metric is added.
Convex setNarrower topic: Its affine structure defines segments without requiring a chosen origin.
Finite geometryNarrower topic: Finite affine spaces arise from vector spaces over finite fields.
Jacobian conjectureNarrower topic: Polynomial maps in the conjecture act between affine spaces.
Ax–Grothendieck theoremNarrower topic: It is the domain and codomain in the theorem.