Once you’ve removed all of the Windows Server 2003 domain controllers from your environment, you can upgrade the domain and the forest functional levels.
I covered what the benefits were of raising the domain and forest functional level to Windows Server 2012 R2 in a previous post http://windowsitpro.com/windows-server-2003-end-support/understanding-active-directory-changes
The key to understanding functional level change is that your options are dependent on the operating systems of the domain controllers in use. If you’ve got some Windows Server 2008, 2008 R2, or 2012 domain controllers in the domain, you won’t be able to upgrade to the Windows Server 2012 R2 functional level until you retire them.
Also, if you do raise the domain functional level to Windows Server 2012 R2, that functional level will define the minimum operating system of any future domain controllers. Put another way, if you have a Windows Server 2012 R2 functional level domain, you won’t be able to add domain controllers running Windows Server 2012, Windows Server 2008 R2, or Windows Server 2008 to your domain.
The other thing to remember is that the minimum domain functional level determines the minimum forest functional level. If you have a forest with 5 domains, with four of the domains running at the Windows Server 2012 R2 functional level and one of the domains running at the Windows Server 2008 functional level, your highest forest functional level will be Windows Server 2008. You won’t be able to upgrade the forest functional level to Windows Server 2012 R2 until that domain running at the Windows Server 2008 functional level is upgraded to the Windows Server 2012 R2 functional level.