The Overshoot option causes a spotlight to flood beyond its falloff area, and cast light in all directions. With Overshoot turned on, the spotlight casts light in all directions but casts shadows only within its falloff cone. See Spotlight Parameters.
Above: No overshoot
Below: Overshoot turned on
The Overshoot control effectively turns the spotlight into a hybrid between an Omni light and a spotlight. With Overshoot set, the spotlight casts light in all directions as an Omni light does but still casts shadows or projections as other spotlights do. The shadows and projections are limited to the falloff region: outside the cone of the spotlight, Overshoot casts light but does not cast shadows or projections.
Overshoot is useful when you want to light a large area but need to cast shadows in only a small part of that area. Set the falloff to include the area where shadows must appear, and then turn on Overshoot to light the rest of the scene. This technique can reduce the size of shadow maps and thereby improve rendering speed.