In geometry, the transformation of points from one space to another.
One example application is cartography, where geographic features such as coastlines, rivers, political boundaries, etc., that lie on a sphere (okay, the earth isn't quite a sphere) must be rendered on two-dimensional plane (i.e., a map). Many kinds of projections have been invented for this task, each with its strengths and shortcomings (e.g., preserving land areas or preserving direction), which may depend on the size of the region being projected.
A simpler application is photography, where the three-dimensional world is transformed into a two-dimensional plane using the perspective projection. A line (called a line of sight is drawn between a special point (called the focal point and each point in the scene, and the intersection of these lines with a specially designated plane (termed the focal plane) forms an image.
An even simpler application is non-perspective architectural drawings such as blueprints. There is no focal point; lines of sight are all parallel and intersect the focal plane orthogonally. Thus, this is usually termed an othogonal projection.