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A retrograde orbit is an orbit the opposite of the usual direction. Orbits are typically in the same general direction, perhaps with some small inclination, and in the same direction as the host star's rotation. The presumed reason is that the whole system began from a spinning cloud which naturally formed into bodies circling in the direction the cloud was spinning, a consequence of the conservation of angular momentum. Given a reference plane, orbital inclinations outside the -90° to +90° range are characterized as retrograde. The term prograde orbit indicates an orbit that is not retrograde.
Neptune's moon, Triton has a retrograde orbit, which is considered evidence that it is a captured minor planet. Among the early extra-solar planet discoveries were retrograde hot Jupiters, i.e., hot Jupiters with retrograde orbits.
Retrograde rotation is rotation of the planet or moon in the opposite of the expected direction, and prograde rotation means in the expected direction, i.e., rotation in the same direction as the orbits. Venus has a nearly-fully retrograde rotation, i.e., with a rotation axis that is typical for solar system planets, but turning in the opposite direction. Uranus and Pluto each have an axial tilt a bit outside the -90° to +90° range, their orbits also termed retrograde.
In astronomy, the term retrograde motion is used for something quite different, that can be called an illusion: occasional motion of solar system planets across the sky that is opposite of the usually-observed motion. A planet's position in the sky is caused both by the planet's orbit and the orbit of Earth, and the motion across the sky becomes retrograde when the Earth is passing the planet: for example, Mars takes longer to encircle the Sun than does Earth, so the Earth regularly passes Mars during their orbits. This retrograde motion is merely the appearance of the Planet's motion when viewed from Earth.