My White Rodgers 1F95-1271 thermostat screen was blank, and I noticed it came back on when removed, blanked again when installed. Batteries are good.

Their phone support had me disconnect "C" and reinstall. It works and the tech said not to worry about it.

What is terminal "C"? Should I have an AC tech take a look?

Can I use it until the tech arrives?

C = common
is used so that your tstat draws it main power to work from the transformer in your airhandler, its not necessary but nice that you don`t have to worrie about changing the batteries once a year, use it without the c hooked up, from now on if you like

C may have shorted to another terminal. Without C your batteries won't last as long. C is optional. Another possibility is a bad thermostat.