They're saying that as opposed to virtual servers or server instances, they have actual physical servers.
This isn't a recent term at all? Back in the 90's people were selling dedicated, unmanaged hardware as "bare metal" servers. Bare metal simply refers to the fact that they're handing you an assembled server only -- you need to install an OS and configure it.
I've seen this term used a lot recently to describe dedicated servers, even Leaseweb does it now. Someone please tell me why.