I think GP's use of "hand-clocking" to refer to the factthat the z80 can run on a very low clock rate, to the extent that you can have a hand switch that sends individual clock pulses to the processor. This can be useful for testing purposes as well as for low power operation in embedded applications.

http://www.thomasloven.com/blog/2013/01/Z80-Tester/

As the Z80 doesn't use dynamic registers (I think basically the only "modern" CPU to make this decision) it doesn't need a minimum clock signal speed to refresh the registers as every other CPU does.

This means you can rig up a push button switch and manually advanced the clock one button press at a time.

To me that's super cool. It also makes them really easy to debug.