A hyperbola is a type of conic section that appears as two mirrored, open curves. It is defined as the set of all points where the difference of the distances to two fixed points (called foci) is constant. Hyperbolas can be represented by the equation in standard form: ((x-h)^2/a^2 - (y-k)^2/b^2 = 1) or ((y-k)^2/b^2 - (x-h)^2/a^2 = 1), depending on their orientation. They often arise in various fields such as physics, engineering, and astronomy, particularly in the context of orbits and trajectories.