What is the significance of the /admin switch in mstsc.exe?

The (deprecated) MSTSC /console switch is now called the /admin switch:

In both Vista SP1 and Windows Server 2008, the Remote Desktop Program has been updated to version 6.1 (6.0.6001) and one of the changes is that the functionality previously associated with the /console switch is now called the /admin switch.

By using it you're connecting to the Console Session on the server.

From http://support.microsoft.com/kb/947723

When you connect to a server that does not have Terminal Server installed.

If a member of the Administrators group starts a Remote Desktop session to a Windows Server 2008-based server that does not have the Terminal Server role service installed, the following conditions are true for the remote administration session:

• Time zone redirection is disabled.
• Terminal Services Session Broker
• (TS Session Broker) redirection is disabled.
• Plug and Play device redirection is disabled.
• The remote session theme is changed to Windows Classic.
• Terminal Services Easy Print is disabled.

When you connect to a server that has Terminal Server installed

If a member of the Administrators group starts a Remote Desktop session to a Windows Server 2008-based server that has the Terminal Server role service installed, they must use the /admin switch to connect to a session to remotely administer the server. The following conditions are true for the session:

• You do not have to have a TS CAL to remotely administer a terminal server.
• Time zone redirection is disabled.
• Terminal Services Session Broker redirection is disabled.
• Plug and Play device redirection is disabled.
• The remote session theme is changed to Windows Classic.
• Terminal Services Easy Print is disabled.

Actually it's a little more complex than just a replacement for the /console. Check out http://support.microsoft.com/kb/947723 for more info. /console is designed to connect you to session 0, but session 0 isn't used the same any more and is no longer needed.