What it comes down to is what would you do to optimize a server running WordPress that you normally wouldn't do on a server running anything else? Not much.
There really isn't much other than pre-installing WordPress and a few plugins for you. Maybe they could provide some custom hosting features or proprietary plugins as well. Just about any other optimization, backup, security, caching, or other enhancements are things you would do anyway and would benefit any web server application.
I'm sure there are plenty of "WordPress Optimized" hosting companies that do nothing more than pre-install WordPress for you.
On the other hand, it could be that the hosting company has a very good knowledge of WordPress and knows how to address common issues and provide good customer support. That is certainly something for which it would be worth paying extra.