When you deploy your app locally, by default a HSQL database is used, which is stored in the deployment folder of your local checked out model.
When running on a free app it can be found in your online project under environments
But I guess you want to open it and see the database table(s) and records. Right?
In that case viewing the local database can be done by running your app locally and open the databaseviewer from Studio Pro
You can view the built-in database where your data is being stored by navigating to:
Console → Advanced → Start built-in database viewer
This will open the database viewer where you can see al the tables in your database.
You can also run queries in the database viewer to view or modify data stored in the tables.