The continental margin represents the transition zone from the shoreline of the continent to the abyssal plain of the ocean floor and includes the continental shelf, continental slope, and continental rise.

Cross-sectional illustration of the continental margin.
Passive continental margins are those where no plate boundary exists between continental and oceanic crust. In other words, the continental crust and the oceanic crust are part of the same tectonic plate. No plate boundary means no constructive geologic forces. Instead, destructive geologic processes dominate and the landscape has been worn down by erosion. Passive continental margins are characterized by subtle topography along the coastline, no volcanic activity, little to no earthquake activity, and a wide continental shelf.
Illustration of a passive margin.
Passive continental margin (By Joshua Doubek (Own work) [CC BY-SA 3.0], via Wikimedia Commons).

Active continental margins include a plate boundary that separates continental from oceanic crust. Interaction of the plates along the plate boundary drive constructive geologic processes, such as tectonic uplift and generating magma, resulting in pronounced topography with hills, mountains, and volcanoes. Active continental margins generally have a narrow continental shelf.
Active continental margin.

Active continental margin (WikiCommons).

The map below shows the locations of an active continental margin along the western margin of South America. A trench separates oceanic and continental crust. The passive margin is along the eastern margin of South America, where there is no plate boundary between continental crust and oceanic crust, and the continental shelf (indicated by the lightest blue color of the oceans) is relatively wide. Similarly, the transition from continental Africa to the Atlantic Ocean basin is a passive continental margin because there is no plate boundary separating the oceanic from the continental crust. One has to travel thousands of miles from the shoreline before reaching a plate boundary in the middle of the Atlantic Ocean.

World map showing plate boundaries and the locations of an active and passive continental margin.