Why might an instructor in a small aircraft choose to descend with a substantial yaw on a first lesson? Many years ago I took an introductory free (+fuel) flying lesson in a dual-control small aircraft (instructor in right seat) at a small city's municipal airport. There was a third passenger in the back. Near the end there was a report of a helicopter near the airport but there was some confusion as to the location.

When the instructor took us back down they did so in an unusual and exciting way, possibly to impress the third passenger, possibly trying to get back to the ground as quickly as possible because of the situation with the helicopter.

We were descending pitched substantially down, looking at the ground in the distance and with a startling amount of yaw with the right wing advanced by (estimate from memory) 20 degrees! 

Is there a name for a descent like this? Are there standard reasons for it?
Sounds like a Forward Slip. It is not an unusual maneuver. It is very useful in order to descend faster than normal (Vertical Speed) without increasing your airspeed. The maneuver reduces the amount of lift generated while at the same time creating a large amount of drag by presenting the broad side of the fuselage to the relative wind. 

Did the instructor happen to reduce the throttle to idle right before the maneuver?

It is also a great maneuver to practice in case a no-flap landing is needed due to flap failure.