A strange thing happens at the gaming table.
Dice and numbers and intentions resolve to create a narrative. With little more than associated statistics and semi-descriptive mechanics, a group of people mutually decide how imaginary things happen.
It was a major epiphany when I realized how much control I have over that point of translation, when the "hit for 6 damage" turns into "the spike of bone lances out from the narwhal's jaw, impaling the already-bloody cleric."
Not just in description, but in the chains of causation that lead to an attack missing or hitting.
Interpreting the Roll
Here's an example:
A rogue is climbing a wall. The rogue has +12 on her climb check and the act of climbing the wall is DC 15. The rogue rolls a 2 on the d20 for a total of 14. Failure.
This can be described in a couple of ways.
Alice the DM: "You scramble up the wall, but in your haste, your sweaty fingers slip on the rocks and you go crashing to the ground."
Bob the DM: "You expertly scamper up the wall, but a sold-looking stone suddenly betrays you, crumbling and sending you crashing to the ground."
The difference is in WHY the check failed.
There's an assumption here--one that Alice is following--that the wall is constant (because it has a constant DC) and the rogue's climbing is what's variable (because the skill bonus is modulated by a d20 roll). But that's just mechanical--you can easily switch it up so that the fixed attribute is on the rogue, and the wall is what's variable.
Look at the rogue again. +12 to climb checks. That's an expert climber right there. That's not to say that even expert climbers don't make mistakes, but sometimes it's the wall's fault, too.
Bob assigns blame for the failure on the wall (and has the side-effect of making the character not sound like a shitty climber, which may be desirable). But this is just one way the DM could choose to interpret the die rolls. An old would could have opened up. The character could have suddenly lost their nerve. An enemy could have thrown something.
A couple of these intrude on what the rules "normally say" is possible.
The old would couldn't open up because there's no rule for that, just as there's no rule for losing your nerve while climbing a wall made from mortared skulls. Enemies can't throw objects on the players turn unless they have a readied action.
But a DM may just choose to sweep all of this under the rug in the name of "flavor".
Postulate: As long as a DM's flavorful descriptions don't change the outcome of the game, they can and should say whatever they want. In fact, these liberties are part of the DM's job.
I'm of this school of thought.
Of course, if you constantly describe your players as incompetent slobs, they may get sick of your denigrating DMing. (What is this, Warhammer?) Likewise, putting words in their character's mouths or assigning them intentions without the player's permission is a no-no.
But everything else can be described as you see fit.
This is harder than it sounds.
It requires you to actually step back and think about what's going on as a whole and then choose the best way to describe it.
Don't think that you have to describe it with the granularity of a single dice roll.
Pete succeeds on a to-hit roll.
Alice the DM says, "You swing your axe overhead, knocking aside the yoblin's shoddy shield. . ."
Pete rolls 6 damage.
Alice the DM says, ". . . and your axe cleaves his skull, bursting it like a rotten melon."
Pete rolls to hit, and rolls to do 6 damage.
Bob the DM says, "Your axe shreds the yoblin's shield like cardboard, continuing through to sever two of fingers against a yellow skull and finally bury itself deep in the creature's brain."
Charlie the DM waits for everyone to roll their hits and misses.
Charlie the DM says, "Ollie thrusts his spear straight at the yoblin's heart, but the creature jumps nimbly out of reach. His attention on Ollie, the yoblin nearly bumps into Pete, who expertly kicks the creature's shield to the side and severs its sallow head with a businesslike swing of his axe.
I'm not proposing that any of these styles of DMing are best. I'm saying that it behooves DMs to remember that these are all optional ways to flex the DMs duty of description. In all three cases, the dice rolled the same numbers, but the DM chose different crayons to color the results.
Alice's method of by-the-roll interpretation is a little exaggerated, but this point-by-point description could be beneficial to a first-timer who is still figuring out what each roll is supposed to represent.
Bob's method is a middle ground, and is probably closest to how most of us DM most of the time.
Charlie's method is another extreme, since he waits for all the dice and damage to be settled before describing anything. This creates a disconnect, and probably isn't advisable for groups with short attention spans, but allows the DM to craft a scene with more precision and interpretation, more epic, more dangerous, more whatever. The DM can also use this method to make players who miss their attacks feel more useful (or less, depending on your intentions).
So next time you DM, consider the actual point where the dice manifest themselves into narrative. Consider what sort of combat you want to evoke (leaping after giant crickets? hammering at the slabs of an earth elemental?) and try other points of narration.
God, that's an ambiguous name for something. Mechanic/Narration Translation Point?
Which attack was more expertly executed? One that hits by a narrow margin but does 6 damage? Or one that hits by a large margin but only does 2?
That's your responsibility, DM.