what do you need to know about offline editing?.
Basically you need and arcgis online account. If you are using hosted service, you will have to added the hosted service layer to arcmap,
Create a local copy for edting and it is nornally in a folder on your local machine ...
C:\Users\Administrator\Documents\ArcGIS\FeatureServiceLocalEdits\DukuCapture\fs9FBD7E0D4132411C8432FC4C35F7A750.gdb (something like this).
you can work with it offline and once done,synchronize local edits with server
Hope this helps.