Sean sent me a PM and asked me if I might take shot at explaining Parallel Compression ( from here on out, we'll refer to this as PC, and not as a refernce to my esteemed colleague PC/ Marco. ;) ). Sean thought that perhaps those who are newer - or more novice mixers - might benefit from an explanation.
There may be some reading this who might have heard of it - but don't know exactly what it is - or those who do know what it is, but who don't really know how to set it up in a DAW platform, and then, finally, how to use it.

First off, what it is:

"What" it is, is actually very simple, really. It's the process of combining an uncompressed - or lightly compressed signal, with a much heavier compressed version of the same signal in the same overall mix.

For this example, we'll use a kick drum track - with no compression inserted on it - for our examples.
So... let's say you have a kick drum that you feel needs compressed. You like the sound of the kick, but you'd like to get a little morte control over its transient, "peaky" nature.

We could simply insert a regular compressor ( whichever your compressor of choice is, it doesn't matter for this), and then, by tweaking the settings of the compressor, find a place that we think works, and that sound pretty good.

But something has occurred, and it mght even be subtle, but something has changed about the tone of the kick... hmmm... maybe it doesn't have the same "oomph" to it... or maybe that little click, that 'presence" that allows the kick to cut through the mix.. that area up around 3k . has now disappeared. Well, guess it's time to adjust the settings of the compressor... okay, so we'll reduce our attack time on the compressor, which lets that 3k click come back, but now, it's kinda peaky again, and maybe even a little "frumpy" sounding, too.

This is occurring, because much of the time, when you insert gain reduction directly into a track, it will affect the tone and the characteristics of the track; because you are changing the transient and sustaining nature of the instrument. You are reducing the gain - which is precisely what a compressor is meant to do - but you are also changing the attack of the signal, as well as the release and the sustain.
If you are working with something like a kick or snare, depending on where your inserted compressor's settings are at, you can end up dramatically changing the tonality of that instrument.

So, what can we do? Enter Parallel Compression ...

PC allows you to "blend" the compression without affecting or altering the tone of the original signal, because the original signal is still in the mix.

here's the how and the why...

So, we have a kick drum track, with no gain reduction inserted at all; we'll refer to this as the "dry" track. Then, we will assign a compressor to an auxiliary channel, ( from here on out we'll shorten that to the accepted and abbreviated "Aux").
Using the aux send of the kick track/channel, we then feed that dry kick signal to the Aux where the compressor resides.

You now have two kick signals to work with in the mix... you have your dry kick track, and you have your Aux with the compressor assigned, to which your dry kick Aux send is routed.
You're not replacing the kick track with the Aux/Compressor channel... you are simply adding a way to control the amount of the GR as it sits within the entire mix on the original track. And because you haven't altered the original kick track in any way, you can keep the sonic characteristics of that track, and then blend it with the compressed signal of the track at the same time.

So, the first benefit to this is that, unlike when you insert a compressor directly into a track, the PC track/channel won't change the tone or characteristics of the original dry track.

Here's another benefit...

Compressors grab low end first. They love low end. They attack it like a swarm of ants at a picnic. They are magnets to low frequencies. If you insert a compressor directly onto the kick track, the very first thing it will do is to "grab hold" of the low end and attenuate that first.
Now, sometimes this can be desirable; say you are working with a kick that has too much low end energy; in that regard, the compressor ( along with an EQ of course) can help, but, it will also change the tone - because the attack and release times of the other frequencies of that instrument can happen at different times. This can cause all sorts of problems with transient instruments that rely on several different frequencies and bandwidths ( "Q's"); so, while you might be able to attenuate your low end, you are also changing the attack time of the higher frequencies because the compressor is paying so much "attention" and is focusing so much on those lower frequencies, because they are presenting the most energy. Because of this, it can throw off the attack, release - and ultimately the sound - of the other dominant frequencies of the instrument.

Once again, PC is a benefit here, because you are never changing the original kick drum track. This allows you to use as much, or even as little, of the gain reduction in the mix as possible, and then blend that processed signal in with the original.

A quick history:
source: https://en.wikipedia.org/wiki/Parallel_compression

Parallel Compression is also known as "New York Compression", because it was - allegedly - first used at a studio in New York during the 70's. It's early implementation and intention was for drums, to "beef up" the sound of the drums (or the drums bus); but as the years passed, engineers found that they could also use this form of compression on bass, piano, guitar amps, and even vocals. These days, there are no real limits to what, how or where you can use PC; you can use it on any track/instrument you like. While it wouldn't necessarily be my first choice for orchestral instruments, there's no "rule" that says that you can't.

In the next post, I'll insert a YT vid where Andrew Scheps explains this in further detail - and he's a really smart guy, who also happens to be able to simplify and explain complex mixing methods in a way that I'm sure is far better than any way that I ever possibly could...

Scheps is a big fan of PC; he tends to use it almost exclusively these days...

And now, I bring you engineer extraordinaire, Andrew Scheps - in 3...2...1...