I know this question is quite old but I found it through Google so I'm sure others will in the future and an answer now will still help them.
I used the Creation Kit to check out exactly what these perks did. It turns out they just lower the modifier that movement has on your Visual based detection chance. By default a "Movement" modifier is part of the Visual detection aspect of sneaking (It is also part of the Sound factor as well, but that Movement stat is different and is based on gear weight, it has no effect from the Covert Operations perk).
The overall Sneak detection chance equation is very complex, having far more parts than just the Visual factor, but I feel is irrelevant to this question as it will only very much confuse the discussion.
Part of the sneak detection equation is "Visual Factor" which has several components. The whole equation is:
Visual factor = Attenuation * VisualContact * Light * Movement *
Blindness * Invisibility
As you can see, part of this equation is this Movement stat. On it's own is sort of an On and Off switch to the detection formula. When you're standing still the value is 0, when moving the value is 1. So moving just adds an extra multiplier to the chance of being detected.
The Covert Operations perk lowers that value down from 1, decreasing the overall effect movement has on your detection chance. The value per rank are:
Rank 1: 0.96
Rank 2: 0.92
Rank 3: 0.88
Rank 4: 0.84
Rank 5: 0.80
Rank 6: 0.76
Rank 7: 0.72
Rank 8: 0.68
Rank 9: 0.64
Rank 10: 0.60
So as you can see, this Perk can nearly cuts the effect of movement on Stealth in half, it's a great bonus when you consider it costs you no manual Perk points, just the collection of some magazines.