The most concise definition I've ever seen or heard comes from Wikipedia, which defines folk music as "musical folklore." Folklore, of course, comprises the stories and culture of a particular group of people. The "group" could be as particular as a family, or as broad as a nation (or the world, if you really want to get esoteric).
In the broadest sense, folk music is any music which gets played and shared among people. Of course, that would encompass all music, altogether. And, since human beings are prone to organizing things into groups, it makes sense to narrow the description a bit.
Traditionally, a more specific definition would be that folk music has referred to songs which have stuck around and remained relevant across generations. Some people have noted that folk songs are the songs we all know (at least in part). These are songs we don't necessarily know where they came from, or when we learned them. Examples:
- The national anthem
- "This Land Is Your Land"
- "We Shall Overcome"
- "This Little Light of Mine"
- The alphabet song
- "Old MacDonald Had a Farm"
- "I've Been Working on the Railroad"
- "Wabash Cannonball"
- "You Are My Sunshine"
When you start to consider the folk songs you know, perhaps you become aware of the way you've learned about the world, and how your worldview has developed. In America in particular, the folk songs I listed above are just a sampling of how we've documented our history and culture in song. Studying folk music can turn you on to the things which generations have deemed important - based on the list above, you'd consider Americans value education, work, community, relationships, and personal empowerment. If you hold that up to the story of American history, that seems about right.
From these examples, it's easy to see how folk music doesn't necessarily have anything to do with the instruments on which it's played, but rather the songs themselves, and the reasons people sing them.
Why do we think of folk music as being acoustic?
Probably because of the way it has been marketed since the middle of the 20th Century.
Recorded music is a relatively new thing. In the scope of American folk music, recording became a simple and essential way of collecting and documenting the songs indigenous to different communities around the country. Before that happened, for example, people in Massachusetts weren't necessarily familiar with the Cajun music of the Louisiana bayou, and vice versa. Folklorists and musicologists had to go out and travel the country, meeting people from different communities and collecting the songs they used in their lives - whether those songs were used to pass the time, to lighten moods while doing hard labor, for entertainment, or to document important events in their lives.
One of the most influential collections of these field recordings was Harry Smith's Anthology of American Folk Music. Alan Lomax's collection is another exhaustive library of American folk music styles and songs.
The people included on these recordings played acoustic instruments often because that's what they had available. In some cases, they lived in areas without consistent access to electricity. Perhaps they couldn't afford electric instruments and the equipment required to amplify them. The instruments available to them sometimes that included guitars or banjos, other times it was spoons, whistles, and other found or homemade folk instruments.
The spirit of these field recordings and very early studio recordings influenced folks like Bob Dylan and Johnny Cash, the New Lost City Ramblers, and others who became hugely influential during the mid-century folk and country music "revival". Granted, it was only a matter of time before those young musicians - with more access and money to afford electric instruments - took the form to electric guitars and amplifiers. But, a strong faction of the folk community remained which insisted that staying true to the tradition of the style meant playing on the same kinds of instruments on which the songs were written.
During the folk boom of the '50s and '60s, professional folk musicians were so popular that the music industry marketed heavily to the "folk audience." And, at some point (which point exactly could fill an entire book), what became marketed and popularly known as "folk music" and what music "the folk" actually played amongst themselves diverged. By the 1980s, the music much of the public considered "folky" mostly comprised of solo singer-songwriters writing original words and melodies on the acoustic guitar. Some of these people (Paul Simon, Suzanne Vega) were clearly influenced by traditional folk music; others (James Taylor, for example) were more likely pop songwriters who used acoustic instruments to create formulaic (highly marketable) acoustic pop music.
What makes folk music different from acoustic pop?
Since I used Wikipedia to define folk music, I'll share their definition of pop music: "commercially recorded music, often oriented toward a youth market, usually consisting of relatively short, simple songs utilizing technological innovations to produce new variations on existing themes."
Taken very loosely, aside from the targeted youth audience, this isn't far from how I'd personally define folk music. However, in practice, the biggest difference between folk and pop music is that pop music is aimed at performers playing for an audience. It's akin to the difference between someone making a speech, and someone having a conversation. The speech-maker would be the pop singer; the conversationalist, the folksinger.
This is not to say that pop music is culturally irrelevant or devoid of any intellectual or creative value. Quite the contrary, looking at the history of pop music is an equally respectable way of following the history of American culture and thought. It's simply a separate form. Where folk music is the musical voice of a people, pop music is their reflection in the mirror.