For writers of speculative fiction (fantasy, science fiction, etc.), extrapolation is the foundation of good world building. Or maybe it's the second floor. I'm not keen on the metaphors today, but it's definitely important.
Okay, so what is extrapolation? Roughly speaking, it's the process of projecting and expanding known information into an unexperienced area to arrive at conjectural knowledge.
For world-building writers, the "known information" can be divided into two categories:
#1: Rules, history, and status that you (the writer) have created yourself.
#2: Rules, history, and status that the writer did not create, but that are an implied part of the world.
In my own reading experience, it's #2 that trips people up. Most science fiction (and a fair share of fantasy) takes place in our own future or another (possibly nearby, possibly interacting) part of our own universe. But even stories that are set on an entirely made-up world are going to be filled with human beings-- or a recognizable analog thereof.
Humans are clever, inventive, greedy, organized, and often foolish. Some are cautious and some are risk-takers. Throw them a bit of new technology (or magical power) and they will demonstrate every one of these qualities in horrifyingly unique ways.
For example, in I, Robot (the film version), technology has advanced sufficiently to produce stand-alone humanoid machines called 'robots'. These are agile, mobile, and intelligent enough to speak fluent English. Let's make a list of some of the "known" information:
(type #1) Advanced, high-speed artificial intelligence
(type #2) Humans like to go places in a hurry, and are known to use automobiles
(type #2) Humans like to be safe
Given this, the writers (presumably) considered the question of how people get from place to place. They conjectured (extrapolated) that people would stick some kind of robot brain inside their vehicles and let it do the driving.
For a counterexample, let's consider the Star Wars universe, where a partial list might include:
(type #1) Advanced, high-speed artificial intelligence
(type #1) Abundant energy and advanced motive technology (levitation devices, space travel)
(type #2) Long-range, guided weapons already existed in our own 20th century
Given this, a very obvious conjecture is that the war-making parites in the Star Wars universe would have the capability of launching fusion bombs from a distance of many miles, if not many light years. And yet, the climactic field battles in Phantom Menace and Attack of the Clones bear more resemblance to medieval warfare than anything remotely modern. Extrapolation fail.
When to not bother with extrapolation
Basically, you shouldn't bother if you don't need it and/or really don't want it.
A six-page science fiction short story called Ned's vacation to Mars is likely to have such a narrow focus that the details of a Mars-vacationing future aren't relevant. If Ned only came to Mars to resolve a love triangle, then it's not important to extrapolate the existence of competing travel agents, asteroid settlements, or the Martian independence movement.
The great J.R.R. Tolkein provides a study in contrast for the use of extrapolation. His society of hobbits, for example, makes a great deal of sense based on their implied similarities to humans: They build homes, brew beer, and use modest technology (such as mill working); their society is organized with a few vague laws and many strong customs; and they spend most of their time growing and eating food.
But the elves make no sense at all. They live thousands of years and do practically nothing. They haven't developed any technology (not even the eco-friendly kind); they've never explored, much less mapped, the eastern part of Middle Earth; and as far as the reader can tell, they don't even have farms.
What's more, these physically present higher-order beings are almost entirely ignored by human societies in the third age. They have the dangerous trait combination of mysterious wealth and physically apparent difference. There ought to be regular (if failed) military expeditions to conquer and plunder their lands. There should be less hostile but equally greedy efforts to open their borders to trade (think Commodore Perry and the opening of Japan). There should be a cult of elf-worshippers.
And yet... I'm going to give Tolkein a free pass on this one (I'm sure he's grateful). Partly, the lack of realism can be explained by the elves' non-human nature and the dark-ages-like setting that limits contact and exploration. But mostly, it should be noted that Lord of the Rings is not intended as a high fantasy, world-creating work that demands extrapolation. It is an extended work of mythology. It is an Anglicized hobbitized version of The Odyssey.
When extrapolation is useful
Creating a world is not easy. David Eddings wrote that most people who had a notion to try writing fantasy would "eventually decide to take up something simpler -- brain surgery or rocket science, perhaps."
Some of the challenges of world creation are making it easy enough for the reader to follow, having everything make sense, and simply producing a massive volume of original "stuff". But with a very small set of original ideas (e.g., technology or magic) extrapolation provides plenty of solutions.
As an exemplary example, I'll cite the master of world creation, Robert Jordan (The Wheel of Time).
At some point, I speculate that Jordan decided he needed a group of mid-level villains-- i.e., people who weren't necessarily evil, but who nonetheless provided violent opposition to the protagonist. Jordan didn't try to create a new type of magic or an extra deity to define this group, but instead used what he already had:
(type #1) magic, employed by a very small percentage of the population
(type #1) a roughly universal theological belief in the Creator, whose will/goodness/nature is referred to as "the Light"
(type #1) the Dark One (a Satanic sort of counter-deity), worshipped/followed by a small percentage of the population
(type #2) jealousy, fear, and paranoia as part of human nature
From this, Jordan extrapolated the existence of a quasi-religious organization called the "Children of the Light." They seek out Darkfriends (recklessly and erroneously) and they describe all magic-users as "witches", believing that their abilities result from an alliance with the Dark One.
Mission solved. Realism enhanced. Confusing, extra inventions not required.
Later in the story, we are introduced to a group/culture known as the "Aiel". They are a warrior society with a strict code of honor (called "ji e toh")-- imagine a cross between the Klingons and (the Hollywood version of) Shaolin Monks. The Aiel are twice involved in the conquest of Cairhein (one of the nations in Jordan's world), and the second conquest is mostly benign. Also, Cairhein is top-filled with foolish young nobles.
The result is inevitable: Many of the Cairheinen, impressed by their conquerors/liberators, decide to emulate the code of ji e toh. They add their own twists and misinterpretations, and it's disparagingly referred to as "playing Aiel".
This society of imitators was not essential to the plot, but their existence was both realistic and damned funny. More importantly, they added a usable element to the story without requiring any effort from the reader to learn something new.
When extrapolation is required
If you're writing any kind of mystery, especially with a science fiction or fantasy setting, you owe it to your readers to consider all the possibilities.
Let's say Ragnar the Mighty is our murder victim, taken down by a venomous Aldosian Serpent. Nashai the snake handler is the initial suspect. But then the bodies of several nameless peasants are found floating in the harbor, all of them likewise victims of Aldosian Serpent bites. Our intrepid investigator traces the peasants back to Langor the Wizard, who is known to be skilled at mind control, and thus the mystery is solved: Langor controlled the peasants, forcing them to carry snakes to Ragnar; several were killed (and dumped in the harbor) owing to their lack of skill before success was achieved and Ragnar finally bitten.
Extrapolation: Couldn't Langor have simply used mind control on Nashai the snake handler? Or, for that matter, couldn't he have controlled one of the snakes? Or cast a spell on Ragnar and forced him to annoy a bundle of snakes himself?
Perhaps the answer to all three questions is 'no', but you'd better make sure the reader understands the rules of magic well enough to predict that. Otherwise, they will have eliminated Langor as a suspect and feel cheated by the given solution.
A few tools for extrapolation
* People seek power - this should always come up when dealing with magic and technology. If your wizards are few and powerful, will they see themselves as natural rulers? And if not, will those who do see themselves as rulers try to control or eliminate them?
* Every technology spawns dozens of uses - Likewise for every type of magic. If it helps, make a list of human needs and desires and try to imagine the technology/magic being applied to each of those. My list goes something like this: War, mating & dating, earning money (especially if one can displace/outproduce an existing enterprise), health, entertainment, convenience, and recombination (mix it with another technology, especially if that other technology is something generic like computing or transportation).
(Note that if you're writing speculative, futuristic realist fiction, you should be so good at extrapolating these that all of my advice is useless, or you aren't going to amount to anything anyway. This advice is for those who consider themselves storytellers and like to use a science fiction setting.)
* People are social - Any given technology might have its detractors and supporters. Are they organized? Do the users/wizards have a guild? Is there an institution for training people to use this thing?
And finally, if you're shooting for any realism, I offer the following observation: People tend to grossly underestimate the ease with which social organizations are formed, but just as grossly overestimate their power and stability. Nations come & go; they merge & divide. The Illuminati, Freemasons, and Skull & Bones are all real, but so are thousands of quilting societies that you've never heard of. If it helps, think about all the clubs you were involved with in college: those type tend to form quickly and fade quickly; they don't have any lasting institutional power, but they can make a significant impression on individuals and a few events during their heyday.