With Scale up, the resources you run on can only be increased up to the limit of the existing hardware, and the cost for those resources doesn't increase in a non-linear way. 

Scale out means that, instead of increasing a machine's capabilities, you add more machines. With Scale out (also known as Horizontal Scaling), you can scale your application indefinably, and then pay in a linearly–multipling the number of machines by the price per machine.

Scaling out allows you to distribute the processing of requests between several machines dynamically. When there is a high load, you can add machines, and when the load decreases, you can decrease the amount of machines you use. This way, you pay for your actual usage instead of paying for under-utilized hardware.

Azure App Service allows you to set the amount of instances your service runs on manually (Manual scale) or automatically (Auto scale).

In the left-hand App Service menu, click on the Scale out (App Service plan) menu item. In the open blade, you can select the amount of instances you wish your service to run on, or click on the Enable autoscale button to configure automatic scaling: