Microsoft has just released the anticipated update for SharePoint 2013 on premise. Along with fixing some bugs, the key feature for this update is the enablement of improved hybrid search integration with Office 365.
There is also now a hybrid sites feature that consolidates Followed Sites between SharePoint 2013 on premise and Office 365.
In the old hybrid search scenario, you can enable searching of on premise content from Office 365 and vice versa. However, in the old scenario, the indexes are still separate from each other and when you search they are treated as separate.
In the new hybrid search, you can now create a true hybrid index that combines search results from Office 365 and SharePoint on premise in a single index.