Business Connectivity Services (BCS) allows us to publish data from our on-premises SharePoint environment into SharePoint Online using lists or SharePoint apps. One common use of this is to publish sales or performance data held in Excel sheets on-premises to sales employees that connect to SharePoint Online.
Sales people often work out of the office, visiting clients and travelling, so being able to edit sensitive information locally within your organisation and to share that data securely with remote users is an extremely powerful feature to utilize.
Configuring hybrid BCS is beyond the scope of this book but, it was well worth mentioning so you can investigate this feature further yourself. A good place to start is the Technet site Deploy a Business Connectivity Services hybrid solution in SharePoint found at https://technet.microsoft.com/en-us/library/dn197239.aspx.