Light Radius is the radius in which the player sees his surroundings.
Some items increase the Light Radius of the player by equipping them. Charms do not require the player to equip them in order to increase the Light Radius.
In the original Diablo, Light Radius also had a tactical aspect, where it would effect when monsters took notice of the player and would begin advancing toward them to attack them. In this way, characters with a large light radius could trigger monsters from far off and save some walking, whereas ones with a small light radius could sneak past groups of them.
Improving light radius through the magical properties in items means that a character can more accurately see enemies and therefore can avoid surprises and fire from afar when required more easily.