SharePoint 2013 On Premise/Cloud Hybrid Environment

Excerpted from Christopher J Fox's technet blog post: http://blogs.technet.com/b/tothesharepoint/archive/2012/11/09/introducing-the-sharepoint-hybrid-configuration-scenario.aspx

A SharePoint 2013 hybrid environment consists of an on-premises SharePoint 2013 farm and a tenancy in the new SharePoint Online.  The integration of the two allows you to use certain resources from the two constituent environments to build unified solutions.  These solutions then run seamlessly across the two.
A SharePoint 2013 hybrid environment supports these features:

• Search
• Business Connectivity Services from SharePoint Online to SharePoint on-premises

As of the SharePoint Conference 2012, you can find information on SharePoint Hybrid Environments and links to downloadable white papers and poster here on TechNet.
Hybrid content for the SharePoint Conference 2012

• Configure a SharePoint 2013 Hybrid Environment -  A whitepaper  that describes how to configure a hybrid environment that integrates SharePoint Server 2013 and Office 365 with single sign-on, identity management, and bi-directional federated Search
• SharePoint 2013 Business Connectivity Services Hybrid Overview – This document explains what a BCS Hybrid environment is and why you would use it.  It identifies the components that are involved and explains their roles in the solution.  It also walks you through how a BCS Hybrid solution works.
• SharePoint 2013 Business Connectivity Services Hybrid Poster – A full size poster that explains the flow of data and authentication in a BCS Hybrid environment.