A projective space is a mathematical concept that extends the idea of geometric space by adding "points at infinity." In a projective space, lines that would normally be parallel in Euclidean geometry intersect at these points at infinity, allowing for a more comprehensive understanding of geometric relationships. There are different types of projective spaces, such as projective planes and projective n-spaces, which are denoted as P^n. These spaces are essential in various fields, including algebraic geometry and computer graphics, as they help in modeling perspectives and transformations in a unified way.