Typically when you right-click on an enemy hero, the nearby (500 radius) creeps will agro you, and attack you. When you cast spells on enemy heroes this is not the case.

Orb-Walking involves using abilities that have Unique Attack Modifiers. Select the ability once and click on an enemy hero, this is now considered casting an ability; nearby enemy creeps will not attack you. You can repeat this as many times as wanted. Right clicking the ground to move in between casts of your Unique Attack Modifier is where the 'walk' comes in, and allows you to land more attacks on a fleeing enemy.

Conversely, if you enable auto-cast for the Unique Attack Modifier and right-click on a hero, creeps will attack you.