Depending on the type of object, Radius can mean different things.
For ControlPoint objects (i.e., flags), the radius determines how close a soldier must be to affect the flag. See DisableIfEnemyInsideRadius, DisableWhenLosingControl, LoseControlWhenEnemyClose, LoseControlWhenNotClose, TimeToGetControl, TimeToLoseControl.
For SupplyDepot objects, it gives the range of influence of the resupply object (ammo box, repair pad, medical locker).
For Projectile objects such as bombs, it is how far the blast extends, with the blast's effect dropping off linearly with distance. Specifically, damage falls off linearly with distance from the center of the explosion, going to zero at its Radius. The term is simply (1 - distance/radius). For example, say an explosive pack was put 1.2 meters from center of a vehicle. The damage from the explosion is then multiplied by (1 - 1.2/4), or 0.7. See the Damage Tutorial for more information.
The ExplosionRadius is used to set the radius of effect when a vehicle blows up. Other radius properties of interest: DetectionRadius, DisableIfEnemyInsideRadius, SetEntryRadius, TriggerRadius, UseButtonRadius.
Source and more details