“Locally” installed applications are installed on the hard drive of your computer. You can use the locally installed applications only when the device is physically available.
On Athena, you have many more applications at your disposal. You can use them from any device which has a Citrix client program installed. Working with Athena has the advantage that no software is loaded on your computer and that you can use the latest (or several) versions of applications. Functionally there is no difference between applications running locally on your computer and applications installed on Athena.