The earth's crust is broken into sections, called plates. There are two (2) basic types: oceanic plates which are composed of basalt, and continental plates, which are mostly granite. The continental plates are in motion, and literally bounce around on the surface like giant air hockey pucks. The overall rate may be extremely slow (one to ten centimeters per year), but the long term effect is a continual re-shaping of the surface of our planet.
An active continental margin is found on the leading edge of the continent where it is crashing into an oceanic plate. An excellent example is the west coast of South America. Active margins are commonly the sites of tectonic activity: earthquakes, volcanoes, mountain building, and the formation of new igneous rock. Because of the mountainous terrain, most of the rivers are fairly short, and the continental shelf is narrow to non-existent, dropping off quickly into the depths of the subduction trench.
The North American plate also serves to illustrate this difference. The west coast is the active margin, and is the location of earthquakes, volcanoes, and mountains. The Eastern Seaboard is a passive margin, as is the Gulf Coast. These are the low-relief areas of our continent, and are the locations of such exciting places as New Jersey, the Barrier Islands, the swamps of Florida, and the Mississippi delta.