Recently, we noticed that there was a small bug with a core piece of functionality: the switch for letting Whiplash automatically set Process Orders wasn't doing anything. When we fixed that bug, we learned that quite a few customers were relying on that "incorrect" functionality.
You'd keep this box checked if you want us to automatically start shipping goods as we receive them. You'd keep it un-checked if you want to control when we start shipping a product that's getting stock after being depleted.
In most cases, this is a setting you won't touch unless something about your process or approach changes. The full doc about Process Orders and related settings is here.