Paper is a great medium for visualizing simple designs and mapping out rough ideas. It's common for game and UI designers to use whiteboards or post-it notes to explain their ideas to their colleagues, who'll often carry the design towards a more robust prototype.
However, if the design is complicated, highly interactive, dependent on animation, or if you'd like to create a set of many ideas that differ in small details (such as icon size, button placement, and so on), it's best to migrate to a digital medium.