Can someone provide a dumbed-down explanation for how a plain old recip. saw action differs from orbital sawzall action and whether there's any significant benefit to having the latter? Getting ready to purchase a new one...

I believe the word "orbiting" is the key. If you watch the motion of the saw blade, an orbiting blade is not just going straight up and down; it's got some back-and-forth motion as well. This is supposed to improve cutting and work begtter on certain materials.
Others might have more detail.

Just like the other guy said, standard is back and forth, orbital at the same time angles the blade as it goes. It should cut quicker. I just got an orbital jig saw, it's a feature on the tool I can't live without.