A problem has vexed all role playing games since the hobby's inception: what exactly is it? Poker is a card game in which players wager on the strength of their hands. Chess is a wargame in which each opponent attempts to take his opposite's king. Monopoly is a board game in which each player attempts to bankrupt each of his competitors. This pithy exercise fails to yield a satisfying answer for an RPG like Dungeons and Dragons.
The first problem is that D&D is closer to a simulation that a game. Simulations are abstract machines in which only "interesting" parts of a problem are detailed. Simulations are run over a time to watch how these interesting parts change as various bits of input are manipulated. Simulations end when some endstate has been achieved. For example, a reasonable endstate for a financial simulation that modeling a recession might be when a country's GPD returns to growth. Alternatively, an endstate might simply be "what happens to the model after a running for an hour?"
Right away RPG veterans will recognize the kinship their hobby shares with video games like The Sims. Often, simulations have goals within them that are interesting outside of the desired endstate. In the economic model above, you might be interested in the effects of public debt on employment and bond prices.
What does D&D model? Even a cursory reading of the OD&D or B/X rules shows that combat is the "interesting" part of a fantasy simulation that Gygax and company chose to detail. As has been mentioned elsewhere, D&D grew out of the older hobby of miniature wargaming (which apparently goes back at least as far as H. G. Wells).
Wargaming is most certainly a simulation with very specific endstates: either the material destruction of opposing forces or the capture of some strategic location. The simulation models the combat forces needed to achieve these objectives. In turn, this requires that each component of the force have statistics that compare its relative combat effectiveness to other components available. More concretely, when designing a wargame with light infantry and tanks, you would make the light infantry much weaker than the tanks.
In D&D, nearly all character generation is geared to creating combat statistics. Each of the six primary abilities has some effect on combat. Armor class, class, hit points, saving throws, THAC0, movement, level, experience points, spells and equipement are directly involved with resolving combat. However, there are a few non-combat stats that need exploration. The most notable is alignment followed by the character's name.
Character alignment has always been controversial, even from the game's beginning. On the one hand, alignment serves the needs of combat simulation. You need at least two sides to get conflict. What better source of division than good verses evil? It worked for Tolkien, it works for D&D.
At a superficial level, dividing the game into forces of good (presumably led by the players) and minions of evil (directed by the dungeon master) is a simple way to motivate combat. Unfortunately, this moral dialectic inherently pulls in the broader collection of literature and philosophy that wrestles with this very issue. What do the "good" guys want? Why are the "evil" guys trying to kill the good ones? These "narrative" questions lead to the most notable non-combat aspect of D&D: acting.
To build this non-combat narrative, D&D necessarily borrows from the disciplines of fiction writing and theatre. To make the combat more interesting, drama is created by getting the players to invest some emotion capital into their PCs, primarily through naming the character and perhaps by drawing a sketch of him. The DM can then create situations in which these characters are challenged, which brings in the pre-planned combat.
Narrative without dialog is a little dry, so D&D encourages players and the DM to exchange in-character dialog. It is this element that most bothers me about the hobby.
As an element of simulation, acting is difficult to account for. It is outside the mechanic of dice (aside from morale and reaction checks, which merely set the tone for the dialog). It is difficult to assign experience points to the quality of acting, although some DMs to do this. At worst, this "role playing" devolves into poor community theatre.
Some players wish to enhance the non-combat aspects of D&D. Can characters have sex and children? If the character is a baron, is the daily life of a noble really interesting to role play? Racial preferences that don't directly lead to combat make for "witty" banter, but does that affect the overall simulation?
Refocusing D&D back onto being a combat simulation makes the game a lot easier to understand and explain to non-hobbyists. The thorny issue of "who wins" D&D goes away. A D&D campaign is a combat simulation that tests the endurance of characters through a series of mental and martial challenges.
Perhaps this doesn't roll off the tongue, but I think it encapsulates the game well for me.
Combat has clear goals and outcomes. Acting does not. Combat can be quantified, but acting cannot be. In my campaigns, I favor generals over actors. Some dialog cannot be dismissed, but it is minimized.