For those who just want to quickly see what the tool does, I’ll include a time-stamped link to that part of the Demo here:
https://youtu.be/Kw3bcsmkGuk?t=2145

BlacksMatch recreates a Toe operation with merge nodes, meaning you can now plug in an external image are your black color and it will perform the operation taking each pixel’s value into account as the blackpoint.  

You can control the Multiply, which is how far above the blackpoint the blacks match with stop affecting your midtones and highlights.  For example, if you plugged in 0.15 and had the multiply set to 2, then values above 0.3 remain unaffected.  

The “falloff” or Gamma control just controls the falloff of the curve into your blackpoint color.  if it’s really high, it will act more like a screen or plus (still ending at the blackpoint color times your multiply control), and if it’s really low, it will act more like a clamp.  Your blackpoint will not ever fall below your input color while you manipulate the curves.

There is a preview plotscan button that helps you visualize how your curve is behaving with your settings.  Just move the plotscan picker around and it will sample your blackpoint color at that area and give you an overlay of your curve.  (Don’t forget to turn it off when you are done)

I personally think this is a tool every comper should have in their toolkit, as it’s by far the most controlable way to match your blacks properly!

The settings of the BlackMatch Tool and a wipe from the tutorial:

From – Compositing Mentor