With the release of SharePoint Server 2013 and the new Office 365, SharePoint is increasingly moving towards an “integrated services” architecture in which on-premises SharePoint Server features can be integrated with SharePoint Online to create what is commonly called a “hybrid” SharePoint environment.
New functionality in SharePoint Server 2013 and SharePoint Online enables you to integrate services like Search, Business Connectivity Services, and Duet Enterprise Online across the on-prem/cloud boundary.
Check out this post from Kelley Vice, Microsoft Sr. Writer for SharePoint Server Content Team, for information on:
• What constitutes a hybrid environment
• Why you might need one
• How to find updated guidance to help you plan, design and configure your own: Hybrid SharePoint Environment