A state in which a computer is "thinking" and is currently unresponsive. Not exactly frozen, hourglassing gives a potentially false sense of action on the part of the computer.
Most common on systems running various forms of the Windows operating system. I'm sure Mac/Linux GUI users have their own terms for it.
CSR: You'll have to bear with me a moment, my PC is hourglassing.
ME: Hourglassing, eh? Is that the technical term for it?