My understanding is that $rootScope is some kind of global variable which allows it to be shared across controllers. Factories can also do the same thing. So, why not use a factory instead? When should one use $rootScope and when should one use factory given that they serve almost the same purpose?
The AngularJS FAQ already answers this pretty well here:
$rootScope exists, but it can be used for evil
Scopes in Angular form a hierarchy, prototypally inheriting from a root scope at the top of the tree. Usually this can be ignored, since most views have a controller, and therefore a scope, of their own.
Occasionally there are pieces of data that you want to make global to the whole app. For these, you can inject $rootScope and set values on it like any other scope. Since the scopes inherit from the root scope, these values will be available to the expressions attached to directives like ng-show just like values on your local $scope.
Of course, global state sucks and you should use $rootScope sparingly, like you would (hopefully) use with global variables in any language. In particular, don't use it for code, only data. If you're tempted to put a function on $rootScope, it's almost always better to put it in a service that can be injected where it's needed, and more easily tested.
Conversely, don't create a service whose only purpose in life is to store and return bits of data.