Dwarf Fortress has the kind of story that I love: two brothers pour their heart and soul into an idea for a video game, doing it solely as a hobby for years, slowly gaining a cult following for what becomes an insanely complicated simulation. And that's just the story of how the game was made.
The actual game is about a band of seven dwarves who set out to create a fortress in the middle of an unforgiving world. You as the player are sort of their manager - you tell them what to pack, and once they arrive, you give them orders for digging, construction, and industry. You never command the dwarves individually; you just tell them, as a group, what needs to be done, and at some point one of them will get around to it. If you're lucky. The dwarves have their own things that they want to do - like eating, drinking, sleeping, and partying - so while they are "industrious creatures", it can take them a long time to get around to what you think is a Very Important Task. Like making sure there's enough food for everyone, or locking all the doors before the goblin horde arrives.
There are an incredible number of systems within the fortress. Mining builds up stockpiles of stone and ores (of which there are dozens of types; one of the brothers is a geologist), which become raw materials for your masons, crafters, and metal industry. Cut down trees create wood for the carpenter and furnace, which can transform them into charcoal. A wide varieties of plants can be grown from seeds and eaten raw, cooked into meals, brewed into drinks (all dwarves are alcoholics), or woven into threads and cloth. Sand can be turned into glass, animals butchered for meat and skin for leather making, on and on.
The simulation is complicated by a lot more than just what you can order the dwarves to do. Every internal organ of every creature on the map is modeled. If one of your dwarves gets into a fight with a wild animal or goblin, he might lose an arm, or just a single finger, or bruise his spleen. Each dwarf has his/her own set of hopes, dreams, likes and dislikes, and each dwarf develops relationships with the others in the fortress. When a friend dies, a dwarf might become depressed - or spiral into madness, killing another dwarf and turning his body into a macabre masterpiece of crafting as a form of grieving. Dwarves are weird.
There is no real way to finish the game; all that you can do is have fun until all your dwarves are dead. In that, it shares a lot with Minecraft, which it helped inspire. It's a sandbox of the best kind, with a level of complexity that ensures you'll never run out of things to do, and a group of characters to care about and root for that makes it feel a lot less lonely than Minecraft's caverns can be. For anyone willing to spend the time learning how to play ("difficulty cliff" is the most appropriate way to describe getting started), it's endlessly rewarding, just as the Adams Brothers intended.
My favorite embark strategy
After playing a lot of games, I've come up with some general strategies that I like to use. Hopefully these will be helpful to you as you play.
First, when you are planning your embark, don't give anyone skill levels in mining. Anyone can mine - levels just make mining faster, not "better" - and thus mining is the perfect labor to give to immigrants that you don't know what else to do with. When you're starting out, just make sure that you have three or four copper picks, and allow anyone who wants to mine to do so. Similarly, there's no need to spend 100 embark points on an iron anvil. It's very hard to get a metal industry up and running in less than a year, and by the time you're ready, a trade caravan will have arrived. Sell them some mechanisms (trade caravans love mechanisms) and you'll easily be able to afford one. If the caravan doesn't have any anvils, then you'll just experience Fun (i.e. losing) and start over.
Two military dwarves as part of your embark is probably a good idea; they can mine when you first arrive, and then start training up a squad once you get more dwarves. Similarly, you'll want one proficient weaponsmith and one proficient armorsmith to equip that squad once metalworking comes online. You don't need to assign any skills in carpentry or woodcutting, either. Instead, put those points into masonry, mechanic, and stone crafting skills. I like to give my expedition leader an extra point in appraisal and as many levels as you can afford in gem setting. More skill in gem setting results in a higher-quality product, whereas extra skill in gem cutting just makes the work go faster. Make one dwarf a proficient mechanic - traps are important and mechanisms make great trade goods - and one at least a skilled planter, so you can make sure your early farming efforts are successful.
I like to take three or four picks, as I mentioned above. A load of bituminous coal is a great idea, if you can get some - one coal turns into nine coke, which can keep your smelters running for a long time while you mine for more. Don't take any axes. That means you won't be able to cut down any trees until a caravan comes or you start metalworking (which, because you don't have an anvil, means you need to wait either way), but that's ok. Start by making everything you can from stone - tables, chairs, doors - and once you get axes, get to work building beds, barrels, and charcoal. Take plenty of plump helmets and plump helmet spawn; they're edible raw and they can be brewed into alcohol. Grab a random assortment of meat and fish to give you some food for starting out and, more importantly, one free barrel for each type of food you buy. Two cats and two dogs, one of each gender, three or four turkey hens and one turkey gobbler for eggs, and if you want to start with butchering early, a few sheep can give you wool, leather, and meat all in one.
That's about it. Be sure to give your group a good (or random) name, and then strike the earth!