This is one of those techniques that can really push you over from intermediate to pro. You need a good grasp on compression: what it does to your instruments and how it affects their texture. Parallel compression is simple, yet subtlety is what makes it work, you need good ears for compression for this to work in your favor.
The essence of parallel compression is immediate and delicate control of the different textures in your recordings or even synths. You make a compressor for different elements of the instrument. In drums it is your punches, your transients and sticknoises, your long releases on snares and the color of all noises: bright, muddy, etc. Sometimes a compressor will affect multiple qualities (but not all of them). Then you make your compressors exxagerate the elements you choose separately. Then you mix the compressors in a way that you find pleasing.
That’s what I’ve gotten out of the video and if you want to get a better grasp for the subtleties with apt explanations from Gregory, then that’s the spirit! Go watch it! If you can’t hear the differences, try increasing your speaker/headphones volume. The effect is subtle so don’t go too loud, just enough to hear the differences described. To avoid any potential hearing damage (in case you do go too loud and/or you listen on headphones), limit your loud volume listening to ~15 minutes or so.