End of Support/End of Life (
EoL) does not automatically make a system less secure or useful, and as much as it pains me to say, I've still got some Windows 2000 machines in my environment (and client's environments) that chug along just fine and aren't a problem.
Having said that, after the end of support, no new patches or updates will be issued for the OS (so there won't be any new Windows/Microsoft updates available for it), and you won't be able to get any technical support from Microsoft on anything using that operating system. That's really all that
EoS means. No more support for it from the manufacturer.
The bigger issue, frankly, is that after 2015, 3rd party vendors will stop supporting it as well (if they haven't done so already), and you'll generally find it unable to run anything new, or update whatever software's on there at the moment. It's also vastly more inconvenient to support, because Windows 2003 is based on an older version of the
NT kernel, with far fewer features than Vista/Server 2008 and above. So you will (if you haven't already) run into a lot more cases where there's one way to manage and administer the 2008 and above servers, that doesn't work on 2003, so you need to create and maintain a second set of processes and scripts and the like.
More trouble than it needs to be, which is really the big reason I try to migrate everything off of Windows 2003 as quickly as possible - it's already hard enough, and more effort than it should be to manage these old systems, and it's only going to get harder, especially after EoS/EoL.