Variations is a SharePoint feature that permits you to synchronize content between different multi-lingual sites in SharePoint by translating the content from the source site to target. It’s a mechanism that can be used to serve the same content to multiple audiences. This feature is available in SharePoint 2013 as well as SharePoint Online.
In SharePoint 2010, variations were also used to provide content specifically targeted towards audiences that used different devices (such as phones) or that required different branding. In SharePoint 2013, you can achieve those results using Device Channels.