What are the low hanging fruits of a SQL Server 2014 migration? I have read about new features and changes of the SQL Server 2014 version. But I still don't know the benefits every server will have by upgrading (from 2008 R2) to 2014? 

Are there any new features / functionality (low-hanging fruits) every instance and database will benefit of immediately, without a single change to the database schema?
In 2014 you get the new cardinality estimator which could see your queries get better plans and therefore execute more efficiently. 

A good reason to upgrade from 2008R2 is that it is on extended support meaning it is unlikely to receive anymore updates and only SQL Server 2012 SP2 + versions are able to operate with TLS 1.2 see here