The first website I found described it a program of fasting and dieting that gives the body a rest so toxins can be removed. Fasting ends by consuming one of their shakes (shocker).
The analogy provided is one of changing oil - you need clean oil. But your body already cleanses itself so what are these toxins that require special treatment?
I found a Wikihow site that describes nutrient cleansing. The key quote here is
"When the body is overloaded with environmental toxins, say smoke, fumes, cleaning chemicals, pesticides from food etc, it may be unable to eliminate them. In this case the body naturally protects its organs by surrounding toxins with fat tissue. Metabolism may be slowed by excess toxins."
Twice the first company I found in the search refers to nutrient cleansing being a practice that has a long history. So what? Here is my red flag that this might be bullshit. Because something is done for a long time is not evidence of efficacy. At best it is evidence that the practice is not overtly harmful. Another example - being a conservation biologist - is the use of animal body parts in "traditional" medicine, like rhino horns for erectile dysfunction. I'm sure this goes back far in human history but if keratin gives you boners just chew your fingernails.
I can see fasting being useful. You lose weight (always good) and you might lose fat (always good). But do you need a special product? Negative.
As for me, I'm ending my spring break with this - and this for you Hitch.