Brushed carving describes turns which are not quite carved, but where the skier avoids big movements that disrupt balance and control and make the tails of the skis slip out.
Some say carving is only edge locked or arc to arc, but the truth is that at high edge angles, the notion of "edge lock" becomes a little blurry, especially in softer snow conditions.
If we were to say that edge engagement starts from 0% (complete skidding out of control) and goes all the way to 100% (edge locked carving on injected ice), brushed carving is towards the end of that spectrum, before edge locked carving, but the point of this concept is not how close it is to edge locked, but the technique used. You can use bad technique and still carve edge locked, happily railing the skis around... that doesn't make it good carving!
Brushed carving is an easy way to control speed while enjoying the benefits of almost carving and skiing in balance, as one can vary the amount or degree of engagement and the skis will perform accordingly.
This is in contrast to just twisting the skis or pushing the tails out, without regards to the turn shape, which is when control is lost: there are many ways to oversteer and skid the skis, see Steering and Oversteering.
The same concept is called drifting1 in the Clendenin Method - with the same idea of controlling the ski with minimal tail displacement and brute force inputs to the ski.