Visibility Determination is the process of deciding whether there is a clear & unimpeded line of sight from one game entity or point in space to another.
Visibility determination may factor into...
Hit detection - determining whether an entity should be affected by ray-like gameplay effects, such as ray picking, beam weapons, or fast/short-range bullets (neglecting projectile physics that cause a bullet to deviate from a straight line over longer distances).
Stealth gameplay mechanics - determining whether a character or security device can see something suspicious or hostile. In this context, visibility may take into account lighting, partial occlusion, or camouflage, to represent whether something is "noticeable" rather than merely line-of-sight reachable.
Light propagation and fog of war - determining which areas of the game world and which entities within it are visible from a particular character's point of view, or receive light from a particular light source. In 2D games this is often achieved by computing visibility polygons.
Occlusion Culling - determining which objects will not be visible in the rendered scene, so they can be omitted from the most intense processing.