Projective Space is a mathematical concept that extends the idea of Euclidean Space by adding "points at infinity." In projective geometry, every pair of parallel lines intersects at a unique point in this space, allowing for a more comprehensive understanding of geometric properties. In n-dimensional projective space, points are represented as lines through the origin in n+1-dimensional space. This means that each point in projective space corresponds to a direction in the higher-dimensional space, effectively unifying various geometric forms and simplifying the study of their relationships.