Basic Jumping provides no benefits to the hero. Jumping, like attacking and other actions slows your max movement speed slightly for 0.5 seconds after landing, standard jump height does not allow you climb terrain, or up short ledges. however some hero's abilites use the jump key to activate (ususally requiring you to press it twice).
Double Jumping is avaiable to some hero's and provides far more agility to the hero in question, it can be used to throw enemies off and make you harder to hit, giving you the upper hand. however, double jumping usually has a cooldown like abilites (can be reduced with CDR). it also allows you to climb ledges and allow for escape.