Short answers, pulled from the story.
Prograde motion means an object orbits or rotates in the same direction as its primary body rotates. Retrograde motion means it moves in the opposite direction. In the Solar System, the reference direction is counterclockwise when viewed from above the Sun's north pole.
Venus and Uranus are the two planets with retrograde rotation. Venus has an axial tilt of 177 degrees, making it rotate almost exactly opposite to its orbit. Uranus has an axial tilt of 97.77 degrees, so its rotation axis lies nearly parallel with the plane of the Solar System.
Venus's retrograde rotation is thought to be an approximate equilibrium between gravitational tidal forces from the Sun, which try to tidally lock the planet, and thermally driven atmospheric tides that exert a retrograde torque. Venus's rotation period is 243 days, and measurements from the Magellan spacecraft and Venus Express missions show it differs by about 6.5 minutes across a 16-year baseline.
Triton is the largest of Neptune's moons and is the only retrograde satellite in the Solar System for which tidal deceleration is non-negligible, because it is large and orbits close to Neptune. All other retrograde satellites are small and distant, so tidal forces between them and their host planets are negligible.
WASP-17b was the first exoplanet discovered to orbit its star in the direction opposite to the star's rotation. A second such planet, HAT-P-7b, was announced just one day later.
A retrograde black hole, whose spin is opposite to that of its accretion disk, produces jets far more powerful than those of a prograde black hole. A prograde black hole may produce no jet at all.