As part of the SharePoint 2013 Service Pack 1, Microsoft has starting to provide some way to implement a sort of hybrid mode – as we can already have with Exchange – with Office 365.
If you go to the SharePoint Central Administration soon after the installation of the SP1, you will see an important notification
As well as a new link/option shown in the Quick Launch menu on the left or in the Central Administration home page
This 2 links provide you a way to configure a first level integration with your Office 365 to use Yammer (as this now included on Office 365 Enterprise plans) or OneDrive for Business on Office 365.
If you go to the Configure Yammer option, you will be able to enable the Yammer integration with your On Premises SharePoint environment
Just hit the Activate Yammer button
After activating Yammer, the Newsfeed link available on the top right becomes Yammer and the link associated changes to point to /_layouts/15/Yammer.aspx, which is a redirection page to your Yammer network – this is the same behavior than when you define Yammer as the Enterprise Social Network in SharePoint Online
Configure OneDrive for Business
The Configure OneDrive for Business allow you to forward your users to their personal space on Office 365 instead of using the On Premises SharePoint platform; this requires of course to associate a SharePoint Online license to the user account to make it work.
Also, if there is already a personal site stored on your On Premises SharePoint, the content IS NOT migrated to OneDrive for Business on Office 365 and this may requires to reconfigure the client side (if your users are using OneDrive for Business client to locally store the content).
You just have to define the Office 365 My Site URL specific to your tenant – which looks like https://<your tenant>-my.sharepoint.com