What changes SQL Server Compatibility Level changes? We had a database and lots of functionality that worked fine in SQL Server 2008 R2.  We recently upgraded both our development and production servers to SQL Server 2014.  Unbeknownst to us, our development server stayed in compatibility mode for 2008 R2, but the Prod box is in Compatibility Mode for 2014.

My question, is where can I find what changed between SQL/Compatibility versions so we will know what needs fixing to maintain functionality.  I know I can set (or have set) the Prod server to compatibility with 2008 but since I don't administer the prod box, I cannot make that call.  My google-fu seems to keep turning up tutorials on how to change the compatibility level, but nothing on what actually changed so I can't tune our queries/procs/functions/etc to work well with the new version.
A compatibility upgrade changes the way the SQL Engine works and has the database level improvements/changes from the other versions.  This doesn't mean you can't use features outside of that though.  For example having a DB in a older compatibilty mode doesn't mean you can't use mirroring or AGs.  

It does mean the query optimizer, newer system provided functions, and other features will not work the same way or be available in some cases.  You will want to ensure your code operates the same way but your DR/HA and operational solutions shouldn't have changed.  

Run your code through the Upgrade Advisor and also read up on the breaking changes.  Read up on best practices for upgrades as well, Thomas LaRock has a good article on it as an example.