Activation and deactivation are actions that can happen to any actor. These allow to provide a higher degree of interactivity with things on the map.
By default, things are active when spawned. The DORMANT flag (which can be set from the map editor) makes them inactive instead. For non-interactive things, the active or inactive status has no effect. However, SwitchableDecoration have Active and Inactive states, to which they are sent as appropriate when respectively activated or deactivated; and monsters are immobile and invulnerable when inactive.
A related concept is the Activation property of actors, which governs how and when they run their action special as well as if it changes their active status or not. With it and the BUMPSPECIAL and USESPECIAL flags, it is possible to create highly interactive objects with very little scripting.