Using a side chain properly could clean up a rough mix, giving room to any instrument that is being mixed into a track. Normally used in basses and pads, or anything with lingering noises. Chained up to more prominent and upfront instruments and ducking the background sounds to give the main instruments more clarity.
A very obvious use of sidechain would be on EDM tracks. The kicks are normally chained up with the basses or synths, causing it to have a breathing effect that you’d always hear on electronic tracks. The easiest form to tell its effects coming on would be melbourne bounce, as the bass is ducked whenever the Kick comes in.
Side chaining can also be used on more miscellaneous stuff such as reverb. Chaining dry vocals to the reverbs and having it duck whenever the vocals are coming through serves as a great way to mix as the reverbs wouldn’t interact with the voices and make it muddy. Of course, there are alot more ways to use side chaining but these are the more common ways in which they are used.