Hi Roberta,
You will need an Enterprise Geodatabase, use the ArcGIS Data Store, or create an ArcGIS Online hosted feature service. Unfortunately, you cannot create a feature service from data residing in a File Geodatabase.
My data is now hosted as a feature service on ArcGIS online. How do I change the settings to make it editable offline? Or since that data was originally from a file GDB, it won't work anyway??
You will need to enable sync on the service. See the section Allow offline editing or collaboration in the below link: