So what is it? I see it often in scenes that other people have built. It in fact may be the reason why I have so much trouble with interior lighting scenes. I just can’t find any information on WHAT spherical reflection does and how to use it properly.
I know there is some limited written documentation on it from Epic which I read, but I honestly still have absolutely no understanding what it does exactly or how to properly use it.
Do you mean the spherical reflection capture actor? 
It’s simple cubemap generator that captures surrounding and then later used for reflections.
Spherical and box reflection capture actors capture the reflection of the static meshes in the environment. You need to use them especially for interiors in order to prevent sky reflections showing on all over the place. You can see their effect by activating/deactivating reflection actors in realistic rendering project.
I don’t think the documentation is *that *limited. This page gives a pretty good explanation: https://docs.unrealengine/latest/INT/Resources/Showcases/Reflections/index.html
Open up all the learning examples and see how reflection captures have been placed.