All apps install locally. It's conventional software. Online access is required only for activation and using specific tie-in services like TypeKit or the cloud file storage.
The Adobe CC apps are installed locally on your machine.
The cloud feature is the storage space provided to you along with your subscription.
@Mylenium, Thank you. So that means when I subscribe for this software, I download and install it on my workstation, active it online, but it runs from my workstation. I can either save my work on my local machine or make use of the cloud storage that comes along with my subscription as Sheena just said above.