My short answer:
Dwarf Fortress is a real-time pause-and-play strategy game that's a cross between Age of Empires and The Sims. You manage dwarves as they build a giant underground fortress and defend it against goblin raids and dragon attacks. It uses character graphics and is very complex.
If they want more information, I continue:
How complex? Through their exploratory mining, my dwarves stumbled upon an underground cavern complex, wherein they discovered a fell beast forgotten since the dawn of time. After dispatching said monster*, they dragged the corpse of the monster to their butcher's shop and butchered it. Taking the fat to the kitchen, they rendered it into tallow. Then, they took some logs to the wood burner, made ashes, took the ashes to the ashery, made lye, and took the lye and the tallow to the soap maker's shop and made some bars of soap. Finally, they used the soap to wash the blood of the beast off their hands.
*with axes they had forged from steel, which was smelted from iron ore and flux stone they mined themselves, in a forge which, for fuel, used charcoal they had made at a wood furnace from trees they had chopped themselves using earlier bronze axes, which . . . oh, forget it.
Ragnar
...Finally, they used the soap to wash the blood of the beast off their hands....
THIS
real time pause and play survival game, where you are the fortress "hive mind"
But yeah, this pretty eloquently sums it up.
I'd have to clumsily sum it up this way: an (incompleted) very detailed, fantasy-realism focussed, deep and difficult but fun and immensely flexible strategy/war/construction game that may have very little in the way of graphics, but nonetheless gets disturbingly gory, even more than most FPS games with lots of gore.
How flexible? Gosh... (long list of examples edited) you can build a decimal calculator out of mechanisms inside the mountain if you persist long enough.
How difficult? You will lose and have fun doing it. Or give up, likely because of the FPS.
How fantasy? You get monsters composed out of dust that have a shell and wings.
How gory? You will start to believe
blood=fun. This is a truth in the game's context, but you should take care not to get locked up in a mental institution if you play the game too much.
But usually it just helps you show them. And the number one way of blowing anyones mind GUARENTEED is to scroll around the fort and demonstrate the Z-level. The Z-level alone confuses and astounds all minds initially, for some odd reason.