OK. If everyone's sitting comfortably: then I'll begin...
Once upon a time, when men were real men and women were real women and cats ruled the earth (I made the last bit up but it could be true) people took pictures using boxes that had lenses at one end and light sensitive film at the other. The boxes had shutters controlled by clockwork and there were no electronics in sight. So to work out how to set the shutters (or the apertures) someone invented an electric meter to measure the light. To begin with you pointed the meter at the greyest item in the scene (because everything was shades of grey in those days) and the meter would indicate how to set the shutter (and possibly the aperture).
Then some clever clogs invented colour film. Measuring the light became a lot more complicated because grey is often in short supply where everything's got colour. But every problem has a solution and the people who made the meters worked out that if you pointed the meter at where the light was coming from, instead of at what it was reflecting off, you could get an accurate idea of how bright the reflected light off those pesky colours was. The only problem was that you needed to diffuse the light you were measuring to allow for the fact you were measuring a point source (the sun) but exposing for a diffuse source (the subject).
So the makers of meters made diffusers to go over the meter sensor. The first diffusers were just opaque pieces of glass but that didn't work too well because the light wasn't just coming from the sun but was being reflected off all sorts of things. People started to make the diffusers in various different shapes to allow for this: domes or little boxes and god alone knows what else. The people who made the Weston meter came up with the oddest shape of all and they called it the Invercone because the main part of it was an inverted cone. and that is what we have here.
Then a bunch of spoilsports came along and invented through the lens metering and... but you don't really want to know all that.