One thing that must be said right away: retrograde motion is not the same thing as apparent retrograde motion. Retrograde motion generally denotes ‘backwards’ motion, and the specifics depend on how the term is being used. A retrograde orbit refers to an object orbiting in the opposite direction that the thing it orbits around is spinning (see image below).
Retrograde rotation refers to an object rotating on its axis in a direction opposite to the motion of its own orbit. For example, when visualizing the orbit of the planets as seen from above the North Pole of the Sun, the planets all orbit the Sun counterclockwise, and most also rotate on their axes counterclockwise; however, Venus rotates on its axis in a clockwise direction, and thus exhibits retrograde rotation.
Apparent retrograde motion refers to the phenomenon that a planet begins moving backwards (e.g. from east to west, rather than west to east) across the sky, as seen from the surface of Earth.
This occurs because, simply put, the Earth is catching up to and ‘lapping’ the other planet during their orbits. As Earth passes the other planet in its orbit, the other planet appears to move backwards. Retrograde motion is something that is observed over the course of weeks or months, as a planet changes place in the sky in relation to the stars, constellations, and other objects in the night sky (that is to say, it is not at all observable overnight). An important thing to keep in mind is that apparent retrograde motion is only apparent. The planet in the sky is not actually moving ‘backwards’ at any point, it simply appears to be in relation to how Earth itself is moving.