An affine plane is a two-dimensional geometric structure that extends the concept of a plane in Euclidean geometry. It consists of points and lines, where points can be connected by lines, but there is no inherent notion of distance or angle. This means that while you can perform operations like parallelism and collinearity, you cannot measure lengths or angles directly. In an affine plane, the properties of parallel lines are preserved, meaning that through any point not on a given line, there is exactly one line parallel to the given line. This structure is foundational in various fields, including projective geometry and linear algebra, where it helps in understanding transformations and vector spaces.