The hyperboloid model is a geometric representation of hyperbolic space, which is a non-Euclidean geometry. It visualizes hyperbolic planes as surfaces shaped like a hyperboloid, allowing for the exploration of properties like distance and angles in a curved space. This model is particularly useful in mathematics and theoretical physics. In the hyperboloid model, points in hyperbolic space correspond to points on the surface of a two-sheeted hyperboloid. Lines in this model are represented by geodesics, which are the shortest paths between points. This model helps in understanding concepts related to geometry, topology, and relativity.