The other night during a game of Scrabble with my family, I played "foam" on a triple word score. I had the opportunity to expand it to "refoam", which would have netted me some extra points, though I didn't dare since I could guess that "refoam" wouldn't be in the official Scrabble dictionary, and so it wouldn't, for the purposes of the game, count as a "real" word.
What makes a word real? If you were to ask people this question out of the blue, I think vanishingly few of them would say that it depends on whether or not the word appears in the official Scrabble dictionary. But many of them would probably say it depends on whether the word appears in some other dictionary, probably the unabridged Oxford English Dictionary, or something like it.
But if you think about it, dictionary writers are constantly adding new words to their dictionaries. Do they invent these new words themselves? No! They find them being used by English speakers. Speakers of English invented them. So were those English speakers using fake words until they were added to the dictionary, at which point they became real words? Of course not! Dictionaries do not come first, speakers of a language and the words they use come first. And dictionaries are not for separating real words from fake words. Dictionaries are just informational tools to help people understand words they have never encountered before. So whether a word is in a dictionary is really a measure of how useful the dictionary writers thought it would be to their readers to have a definition for that word. This set of words—the ones it would be useful to have a definition for—overlaps greatly with the set of words that we might want to call "real", but not perfectly.
So if a dictionary can't tell us definitively whether some string of syllables is a word in a language, how can we tell? Here's a stab: a string of syllables is a real word in a language if it is used by speakers of that language as a word. This is basically the correct answer, but it's also an unsatisfyingly fuzzy one. Suppose I start saying "flarsnip" as a synonym for "plate". Is "flarsnip" now a word with the same meaning as "plate"? Could I play it in Scrabble? Intuitively the answer to these questions is no. "Flarsnip" needs to catch on enough with the speakers of the language to be a word in the language. But which speakers? We all know that different groups of people sometimes use different words to convey the same meaning. For example, the insect often referred to as a "dragonfly" is sometimes called "darner", "darning needle", "snake doctor", "snake feeder", or "mosquito hawk". People playing Scrabble in Arkansas might be inclined to accept different words than those playing in my native New Hampshire.
Then there are words that many English speakers use but that we've all been told aren't words, such as "ain't" (a contraction of "to be" and "not", but close enough to a word for us) or the dreaded "irregardless". Both appear in any complete dictionary of English, albeit with usage notes warning that they are non-standard and to be avoided in formal or careful speech. Are they real words? After all they are in the dictionary and they are used by real speakers of the language! They seem to belong to a special category of word: real words that the authorities tell us should not be real.
So I didn't play "refoam", and when I mentioned that I had wanted to play it, everyone but me agreed that it isn't a "real" word. I protested by arguing that it's easy to concoct a context in which it might be used. Imagine construction workers whose job it is to spray foam on walls. Of course they would use "foam" as a verb: "Pat is foaming the wall," or "Hey Pat, go foam the wall, would ya?". And then one day Pat's boss Chris says, "Hey Pat, I'm going to need you to refoam that wall over there, it didn't stick the first time." Needless to say, this argument didn't convince my competitors, and in the end "refoam" wasn't in the Scrabble dictionary either, which satisfied them. And I agree with them in one sense: for the purposes of a game like Scrabble, it's best to have an authoritative dictionary that settles whether or not a word can be used in the game in no uncertain terms. For the purposes of Scrabble, "refoam" is not a "real" word.
But is "refoam" a real word? Of course it is. Just google it. It's used regularly in the world of speaker system repair. There are 145,000 hits, and several Youtube videos demonstrating how to "refoam a speaker".
The Scrabble dictionary, it turns out, has a whole special section devoted to "self-explanatory verbs with RE- prefix". There are many unexpected verbs in there—"refall", "refeel", "refloat" (each of which my computer's spellchecker automatically changes into something else, by the way)—but not "refoam". If you had to guess, would "refight" be in there? Have you ever heard anyone say "refight"? Have you ever said it? You'll have to check an official Scrabble dictionary to find out.
It's not obvious how to decide which words are real and which are fake. For the most part, the distinction doesn't seem helpful. If a word is being used in a genuine way by a speaker, and is genuinely understood by a hearer, then it's a real word, even though most speakers of the language might not know what it means. Only when a speaker intends for a word to be fake, like "flarsnip" above or many of the words in Lewis Carroll's Jabberwocky, is a word fake (though a fake word may still be a word, depending on how you look at it, see Barbara Partee's discussion of the adjective "fake"). To make matters worse, once you start looking at languages from many different language families, and especially polysynthetic languages in which an entire sentence can be made of a single word, it quickly becomes difficult say what a word even is.