What is "Command Edit Mode"?

This is a toggle state that allows you to use the keyboard to type commands directly into the command line rather than the usual hotkey mappings.  For example, you would type on the keyboard "group 1" rather than "g" "1" to select group 1.

Toggle this on and off using F8 or Ctrl8.  It probably was activated by an accidental button press.

Excellent! Makes perfect sense. Now I l know what it is and how to activate it (F8 I guess) it could be very useful when I forget the hotkey mappiings (alll the time!)

Not sure how you use this with two word commands like "move to."

I get a syntax error when I try to type those with the Command Edit Mode on.

You can enter them with an underscore: Move_To.

But the reason why command edit mode is a bit hidden, is that it's recommended to use hotkey mode: You'll be so much faster. If you have a hard time remembering the shortcuts you can always use the virtual facepanel (tab 7, or in the popup).