The “Open with Windows Explorer” action available for document libraries in SharePoint relies on a WebDav client service (i.e. WebClient) which isn’t installed by default on Windows Server 2008. To get this working you need to install the “Desktop Experience” feature. This can be done by navigating to Server Manager > Features > Add Feature > Desktop Experience (requires reboot).

 

This will also allow you to save Office documents directly into a SharePoint site if you are using Windows Server 2008 as a client.