Here is an animation that I created to illustrate retrograde motion. You'll see Earth and Mars in orbit around the sun and a line going from Earth, through Mars, and to the "fixed stars." A glowing green path will follow the motion of Mars as seen from Earth projected against the stars. (linky)
I always try to use a diagram in my explanations because it's almost impossible to explain it just in words -- it is a very visual phenomenon (well, by definition it's a visual phenomenon).
Text to go along with the movie I've linked to would be: Take Earth and Mars at relatively near points in their orbit and draw a straight line between the two, projecting from Earth, through Mars, and towards the "fixed stars." Earth travels in its orbit faster than Mars, so as the planets move, the line you draw through them will start to slow down relative to the stars. When Earth catches up with Mars in the orbit, Mars will appear to star tot move backwards relative to the stars. As Earth-Sun-Mars form a right angle, Mars will again appear to stop in the sky and reverse direction as they both continue in their orbit.
See, even me re-reading that doesn't make much sense without the movie to explain it. Maybe someone will be able to contribute a better explanation.
However, there are two additional points to make, as well. First, all planets (and asteroids) show prograde and retrograde motion. The duration of each part is dependent upon how far away it is in the solar system and whether it's inner to Earth (Mercury, Venus) or exterior. Also, most planets spend most of their time in prograde motion. Retrograde means it goes against the direction it normally goes. Stars over the course of the night move East to West, as do all objects in normal orbits as seen from Earth. But relative to the stars, the sun, moon, and planets normally appear to go west to east. This is prograde motion even though it's "against" the stars. When the planet flips and goes east to west relative to the stars (again, over the course of one day, everything goes east to west, we're talking now about motion over the course of many days relative to star positions) then it's in retrograde motion.