No need to apologise at all, happy to explain!
Sidechain compression first. Trigger input goes in to compressor, and when that trigger crosses a set threshhold, the volume on another track is affected (usually reduced momentarily). A common application of this in production situations is to feed a signal from the kick drum to a compressor's sidechain on a bass track. This means when the kick happens, the volume of the bass reduces by a desired amount so the kick is clear and not fighting the bass frequencies as much.
And then 'ducking' is just a more extreme version of that, I suppose. Rather than a subtle effect for getting things out the way for a moment, it can be used to create more dramatic volume swells, pulsing etc. It's very commonly used on synths in electronic music, especially house.
The Pill allows you to dial in the depth of the volume drop, and how quickly it recovers again. It's a simple effect in essence but a fairly unique one for pedals, from what I know.
Demo: