What does rod and staff mean?

Answer 1

As with most things of pastoral origin, our modern life is taking us away from familiarity with their use.

The Shepherds Rod was a stick shaped like a club with a smooth round head (the modern analogy would be a scepter) it was used a a weapon to defend the flock from predators, to throw at sheep that were going towards danger, and to examine sheep as they came in at night (to part the fleece to look for parasites)

The Shepherds Staff (or Crook) was a tall pole with a curved hook on one end that the shepherd would use the pole as a walking stick and extend the straight end to guide and drive sheep when needed and the hook to catch the neck of a sheep and bring it towards him.

They were the ubiquitous tools of the shepherd and this shepherding metaphor is used extensively in The Bible and now as symbols of care and authority.