does jotform function as a database?

Yes, JotForm does function somewhat as a database.  Submission data is stored in your JotForm account and can be accessed directly from there. 

https://www.jotform.com/help/269-How-to-view-Submissions

If you require more direct access to the data for web development purposes, we have extensive API to be able to manipulate the data further:

http://api.jotform.com/docs/