The two files are interchangeable, and you can use either one to build your application. index-async.html loads scripts asynchronously, which might give you a faster bootstrap time. index.html loads scripts synchronously, which is often a bit slower, but the intention is that the code is easier to understand for someone learning to use the framework.
To read more about asynchronous bootstrapping, check out the docs here: http://docs.angularjs.org/guide/bootstrap