If a lay person asked me to describe what D&D was, I'd tell them something along the lines of "It's a fantasy game of pretend but you have rules that help shape what you can and can't do, and how well you can do it."
I think, that's what I might say if asked what a roleplaying game was.
I would not tell them "It's a fantasy combat game." I doubt anyone who plays would describe it soley as that, then walk away, assuming the person now knew what D&D is. They wouldn't be wrong, but they'd be incomplete to do so.
I agree. That's how I might describe DDM, though.
I'd mention combat only to elaborate on typical activities pcs might engage in, to explain the need for rules, or to explain the difference between D&D and other rpgs, particularly if the person had already heard something about rpgs in general.
E.g. here in Germany it's not uncommon that someone knows 'Das Schwarze Auge' (The Dark Eye) but not D&D.
Among those who've heard of D&D but never played it, it is a common opinion that D&D is all about 'hack & slash'. That's actually something I'd deny.
I'd tell them that this is a common misconception because many groups play it that way and D&D supports that playstyle very well because of its elegant, tactical combat rules and its roots in table-top war games.
Then I'd point out the changes from one edition to the next, highlighting the evolution of the skill system, culminating in 4e's introduction of skill challenges as a means to resolve non-combat encounters.
But I'd not deny that combat is an important part of D&D. I might even say that it's rare for a session to not involve any combat at all.
To sum it up: First and foremost D&D is a roleplaying game. Nonetheless, it is about combat, but not _all_ about combat (as someone already mentioned in the first couple of posts). A (somewhat) subtle but important difference.