CP^2, or complex projective plane, is a two-dimensional complex manifold that can be visualized as a space of lines through the origin in three-dimensional complex space, C^3. It is a fundamental object in algebraic geometry and has applications in various fields, including physics and topology. In CP^2, each point represents a line in C^3, and it can be thought of as a way to compactify the complex plane. This space is important for studying complex structures and has interesting properties, such as being a non-orientable surface and having a rich topology characterized by its homology and cohomology groups.