A famous definition goes something like "Anything not played by a cow is folk music."
That is almost certainly too broad but it hints at how broad the category really is.
For me folk music, like punk, is an attitude, a philosophy, and a tradition, rather than a specific sound. Folk music usually features a simple low production collection of acoustic instruments. It is music that could be played on your front porch, that doesn't require a huge budget to create. It is usually, but not always, put out by independent artists whose main marketting mechanisms are touring and word of mouth. Folk music lyrics tell stories about real life, real people, real experiences.
Folk music overlaps with many genres of music. Add some twang and it's bluegrass or alternative country. Add a drum set and it's folk-rock. Add a drumset, a mandolin and a bouzouki and it's english folk rock. Add a harmonica and a slide guitar and it's folk blues. Add a lovable asshole and it's anti-folk. Add a horn section and it veers into funk and jazz while somehow retaining it's folky qualities.
Sometimes when I talk about folk I'm generally talking about Americana or American Roots Music. That's a broad terms for any music that draws from old bluegrass, jazz, delta blues, jug band, country, gospel, and guthrie era folk traditions.
Folk music is what folk music fans listen to. Folk music is what gets played at folk music festivals. Folk music is what comes to folk music clubs.
Internationally, folk music of any given country is the traditional people's music of that place. The old dances, the old songs, the old instruments, the old styles. When I talk about folk music I'm generally not talking about international folk music, but rather about Americana and I'm generally, but not always, talking about the new rather than the old.