Server core is a lightweight, capable edition of Windows Server 2008. A lot of baggage isn't there, making more resources available for network applications, while reducing the attack surface area.
Some GUI tools are still available, but one of them that's not is a facility to manage the Windows Update process on the server console. Arguably a sophisticated infrastructure wouldn't need this, and could use WSUS instead. However there are those servers that need some administrative looking-after.
A script to manually drive the windows update process for critical updates is available from Microsoft--follow this link.
The script is dead easy to use, just copy to a server core machine and run using cscript.