Let's face the facts and admit that frequency separation is quite likely the most misunderstood and misused retouching techniques, plain and simple. If you've never heard of frequency separation, then do yourself a favor and browse YouTube on the subject before reading on.
That said, you're going to find copious amounts of information on the subject, usually in tutorial videos that unfortunately tend to contradict each other, channel to channel. It can be quite the enigma. Hence, this video today is my attempt at clarifying what frequency can do, and why the different radius settings matter in how you approach the technique.
With that said, let's also admit the other obvious fact about frequency separation techniques: They vary, and vary wildly, photographer to photographer. Regardless, what I've found is that most photographers never do a side-by-side comparison, as it were, of what different radius settings look like, and how they can affect how you use the technique.
It Can Be Quite Abstract
The radius setting, at least in classic frequency separation setups, has to do with the gaussian blur filter in Photoshop (tho other filters are sometimes used). Using gaussian blur is the most common way to essentially remove the high frequencies from your image, thus creating your low frequency (or "color") layer that is crucial in the frequency separation process. Many discussions have been had on the subject, with no real solid consensus as to what radius you should absolutely use. Most photographers would agree that your image's pixel dimensions are the main variable in determining what radius is ideal. However, what area(s) you plan on working on your image with frequency separation, and how much texture exists in said areas, is also another consideration. Even with the same pixel dimensions on every shot (as would be the case if you used the same camera for every shot, of course) your subject could be framed in a head shot, half portrait, 3/4 framing, or full length, and that affects how much data (pixels) the skin texture has, shot to shot. If you're really into splitting hairs, figuratively, on the matter, then you may use a different radius setting for each of these types of traditional portrait composition approaches.
Since frequency separation essentially helps you separate your color from your texture (mostly), it gives you the power to correct color and tone issues without obliterating texture (especially in skin; but keep in mind frequency separation is useful for many different type of things in retouching). The process you use to correct said color can vary as well, and are directly affected by your radius setting in your filter, which again is usually gaussian blur. A very low radius extracts far more finite texture, but can easily lead to overcooking your skin work into a plastic fantastic disaster if you are too sloppy with it. A larger radius helps preserve more reality, if you will, but also gives you less exact control over what happens in the low frequency layer (or least makes you work a little more to remove imperfections you may not want).
And I haven't even mentioned haloing yet, the well documented side effect of the subtraction process in frequency separation. There are many different ways photographers have found to minimize haloing at higher radius settings, including using the surface blur or median filters instead of gaussian blur, and to be honest those work pretty darn well.
Information Is Not Knowledge
The key thing to know about frequency separation is that it's simply a technical process. In and of itself, it isn't a creative process, it's essentially a tool. And just like a paintbrush doesn't make a painter an artist, frequency separation doesn't make your portraits automatically look good. Accepting that frequency separation is just a tool is the first step in utilizing it better.
To that end, I made the video above to try to illustrate what different radius settings look like, or can look like, and some of my thoughts on why you may want to use different settings depending on your pixel dimensions, your vision, your portrait type, and more.
Let me know if this tutorial helps!