A hyperbolic plane is a type of non-Euclidean geometry where the parallel postulate of Euclidean geometry does not hold. In this space, through a point not on a given line, there are infinitely many lines that do not intersect the given line. This creates a unique geometric structure that differs significantly from the flat surfaces we are used to in everyday life. In a hyperbolic plane, the angles of a triangle sum to less than 180 degrees, and the space can be visualized using models like the Poincaré disk or the hyperboloid model. These models help illustrate the properties and behaviors of shapes and distances in hyperbolic geometry.