An affine space is a mathematical structure that generalizes the concept of geometric spaces. It consists of a set of points and a vector space, allowing for the definition of points in relation to one another without a fixed origin. This means that you can perform operations like addition and scalar multiplication on vectors, but you cannot directly add points. In an affine space, the relationships between points are preserved, enabling the study of geometric properties such as lines and planes. This concept is closely related to vector spaces and is often used in fields like computer graphics and geometry to model transformations and spatial relationships.