From Diablo Wiki
Throw can only be used with throwing weapons, such as throwing knives, javelins, throwing axes, and throwing potions. All but throwing potions can be used as melee weapons, as well as throwing weapons. Throwing potions can not be used without the throw icon.
Some characters possess throwing skills, that require throwing weapons to work,and add special skill effects and higher damage. The Barbarian's Double Throw, or the Amazon's Lightning Fury and Plague Javelin, for instance.
There was a different icon for left throw during game development. This was presumably necessary so characters dual wielding throwing weapons could know which one to throw, but in the final game this is accomplished by setting the throw icon to the left, right, or both mouse buttons.