Most moves are resolved using 2D6, as in base AW. Weapons fire, however, is resolved using a fistful of damage dice. The number of dice is, I suppose, the damage potential of the ammunition being expended (e.g. an assault rifle might produce 3d of fire), and the volume of fire reflects how likely each round is to arrive at the target, and ranges from Incidental all the way up to Concentrated. (The number of steps varies somewhat depending on the version of The Regiment.) I suppose you might think of it as 'volume of accurate fire'.
When bullets land, you roll all the damage dice, and then you cross-index the result on each die on the VoF table. For example, if you're firing your assault rifle out of a car window during a drive-by, that might be 3d Incidental. The Incidental row on the VoF table tells you that each 1 or 2 result has no effect (an outright miss), a 3, 4 or 5 inflicts Stress, and a 6 causes a Wound.
If you're shooting your assault riftle at some one tied up in the back of an industrial refrigerator, well that's probably Concentrated fire. You roll the same 3d, but this time each '1' causes Stress, each 2, 3, or 4 causes a Wound, and a 5 or 6 causes a Critical wound. (Again, this varies slightly by version.)
That's the basic idea.
One thing I like about it is that, against enemy firearms in particular, it's easy for the GM to spray the party by telling everyone to take 2d incidental, without having to be arbitrary about who's the specific target. Keep your head down, grunt!