The Poincaré disk model is a way to represent hyperbolic geometry, which differs from the familiar Euclidean geometry. In this model, the entire hyperbolic plane is mapped inside a circular disk. Points inside the disk represent points in hyperbolic space, while the boundary of the disk is not included, representing points at infinity. Lines in the Poincaré disk model are represented by arcs of circles that intersect the boundary of the disk at right angles. This allows for the visualization of hyperbolic distances and angles, making it easier to understand the properties of hyperbolic space, such as its unique parallel line behavior.