By default, all attachments saved to OURDrive are just copied, not moved. This means they are still attached to your email in Outlook as well.
If there is an attachment on an email you move/copy to OURDrive, then it will stay there inside the email. But if you prefer, you can separately store attachments in OURDrive.
To do this, open an email, and right-click on the name of the attachment. (Note that the Copy to OURDrive button in the ribbon is for the entire email, not just the attachment.)
In the Save to SharePoint window, select the library on the left pane and set the properties on the right pane. When finished, press Save.