A Keplerian orbit (or Kepler orbit) is an orbit (path of an astronomical object gravitationally bound to another, particularly, a repeating pattern) that follows a perfect ellipse, parabola, or hyperbola (i.e., conic section). This is the case for a point mass orbiting another point mass with no other mass near enough to affect them, i.e., an orbit maintained purely by the gravitation between two points (or spherically-symmetric objects). Planets and stars often approximate the behavior of point masses, for approximating spheres whose shells each have its mass distributed homogeneously (spherically symmetric): such spheres act like point masses. Orbits diverge from Keplerian due to additional mass, such as another planet near enough to affect its orbit, and/or a planet's divergence from the even distribution of mass described above, such as having a region near the surface that is especially massive.
Such an orbit maintained solely to gravitational interaction also has a particular orbital speed related to the masses and distance, distance between them and shape of the orbit (Keplerian speed). An orbit may be described as faster or slower than Keplerian if factors other than gravity are contributing, though it still may be in the shape of a Keplerian orbit.
The term osculating orbit is essentially a synonym for Keplerian orbit, most commonly used to describe the theoretical orbit a particular object would have if it were not for sources of perturbation such as other bodies, tidal forces, radiation pressure, etc.