Spotlight
A point light that only shines inside a cone, with a soft edge between an inner and an outer angle.
It has both a position and a direction, plus a cone angle that bounds where the light reaches. Between an inner cone (full strength) and an outer one (zero) the light fades so the edge isn't knife-sharp — the same idea as a stage spotlight or a flashlight. Intensity falls off with distance just as it does for a point light.
Shadows need only a single shadow map, since the light points one way anyway — cheaper than a point light's cube. Spotlights are used for headlights, streetlamps and anything that aims light somewhere. Volumetric variants make the cone itself visible in haze.