Meaning of the empty array in angularJS module declaration

That array is meant to add various module to your current app which is mentioned in your first part of angular.module as string`, You could simply say for injecting various dependency.

You could create an n number of module inside your app for each component of angular & then you could combine them into one single app and you can angular.bootstrap or apply it on page using ng-app directive.

Example

Suppose you have an app which has different component like services, factory, filters, directives, etc. You could create a module for each of them. Just for making separation of concern.

angular.module('myApp.filters', [])
angular.module('myApp.services', [])
angular.module('myApp.controllers', [])
angular.module('myApp.directives', [])
angular.module('myApp.constants', [])

And while appending an component to it you could simply use that specific module of it. Like you wanted to add service then you just add that service into myApp.services by doing

angular.module('myApp.services').service('example', function(){

})

And then inside you app.js you could do combine all of this modules to an single module like below.

angular.module('myApp', [
     'myApp.services', 
     'myApp.controllers', 
     'myApp.directives', 
     'myApp.directives', 
     'myApp.constants'
])

While initializing an app you could simply use myApp inside, that would make available all other module to it.

What is the empty array used for?

In you code you are creating an module which doesn't inject any dependency, [] which means it is independent of any other angular module.

Dependency injected inside the [] is nothing but importing module