Microsoft describes it as:
Server Core: Beginning with the Beta 2 release of Windows Server "Longhorn," administrators can choose to install Windows Server with only the services required to perform the DHCP, DNS, file server, or domain controller roles. This new installation option will not install non-essential services and applications and will provide base server functionality without any extra overhead. While the Server Core installation option is a fully functioning mode of the operating system supporting one of the designate roles, it does not include the server graphic user interface (GUI). Because Server Core installations include only what is required for the designated roles, a Server Core installation will typically require less maintenance and fewer updates as there are fewer components to manage. In other words, since there are fewer programs and components installed and running on the server, there are fewer attack vectors exposed to the network, resulting in a reduced attack surface. If a security flaw or vulnerability is discovered in a component that is not installed, a patch is not required.
A "Core" installation will be completely maintained and managed from a CLI. Looks like you *nix guys will be right at home. But for those of you who run mostly MS shops, this is your wakeup call to start learning how to navigate an OS without the help of a visual interface. For more on this topic, check out thess articles:
"Creating a Core Longhorn Server" from WindowsNetworking.com
"Server Core: Windows Without Windows" from Redmond Magazine.