Before I start to dig in, I need to mention that this feature will make sense to people who know already more than just the basics of Illustrator. It might be a little too complex to follow everything in case you are still starting out, because I don't go into basics here. So I assume you have perfect knowledge of using different Blending modes or Transparency settings, and you also know how the Appearance panel works, applying multiple fills or strokes on one object etc.
This illustration of vases is just one example of where this features comes in handy. As you'll notice, these vases use a special border. It actually consists of two lines on top of each other using a different thickness. The top one is the thinner of the two and is totally transparent, while the bottom one is thicker and has color. You only see the outer line, which is the 2nd border applied to this vase. So this is not created by adding an extra path or object using Object > Path > Offset Path…, as this is how I would have done it if I didn't know this feature. Let's have a closer look…
Applying on multiple strokes
In the above image, I have double clicked on one of the vases which takes me into Isolation mode, because the vase consists of a group containing 2 objects: the vase shape, and the transparent object at the top of the vase. Here the path of the vase is selected which shows its Fill and multiple Strokes in the Appearance panel. As you can see, there are 2 different strokes applied: the top one 1pt thinner than the 2nd one. They are also applied on the Outside of the path. The top stroke has 0% Opacity which makes it complete invisible. So normally this would just hide this stroke and you would see the stroke below it, which is a 7pt wide light green stroke in Overlay blending mode, but with the Knockout Group option checked in the Transparency panel, the area that fills the transparent stroke gets knocked out. Normally this features is applied to a group of objects where the path on top knocks out the path below it, but this feature also works in this situation.
Make sure to target the entire Path
To make this work you need to make sure to target the entire path in the Appearance palette (clicking the top area of the panel where you see the word Path), and then go to the Transparent panel and check the Knockout Group option.
Neutral state checkbox
When doing this you'll notice that this checkbox has actually 3 different states instead of 2 states that you are normally used to. There is a state where the checkbox shows like a dash line. This state is called the Neutral state. As far as I can understand it, the reason why this state is there is because this feature is supposed to work on grouped objects, and so since you can have many nested groups, Illustrator sets this option into neutral state by default. Otherwise each time you modify a grouped situation using this feature, it would affect the appearance. This might make a bit more sense after reading the next paragraph, where I show you how I applied this option on a grouped object.
Applying on a group
Maybe a more typical situation on how to use this feature is when you have 2 objects overlaying each other, and the top object is 100% transparent. In the example above I show you an example of 2 grouped objects: the vase and the transparent area that lays on top. Here I can just check the option after I have grouped both and have the object selected. Of course, you can create this same effect in a few different ways, like using the Pathfinder, but then you wouldn't be able to achieve the same result with the border around the vase using this knockout option.
You might have also noticed another option in the Transparency panel, the Isolate Blending option. If you are curious to know what this feature does, here it is ;) Oh and in case you're also wondering about that 3rd one… don't bother really. I did some research, and it seems to be way too specific and complex, that I can't think of any situation when I would need to use it. In the meantime, I hope you enjoyed reading about this rather hidden Illustrator feature.