Locally. You can send some data to the cloud by using the Firefox Sync service if you like, but it's only a subset of what is stored locally. See: How do I set up Sync on my computer?.

Some Firefox performance data may be sent to Mozilla. To control that, see:

• Firefox Health Report - understand your browser performance
• Share data with Mozilla to help improve Firefox

Am I missing anything?

That is very helpful! Thank you.

In this case we are using "Clippings" the AE Creations plug-in. As the default method is to store it on our Firefox Profiles. Would it make a difference if we simply stored it on another Data Source Location such as our C drive?

I don't understand what you mean by this question:

Would it make a difference if we simply stored it on another Data Source Location such as our C drive?

The extension does allow you use a different local disk location. I'm not sure that has any effect on your cloud question, though.