This article is from the Flamenco for Classical Guitarists FAQ, by Joshua Weage (firstname.lastname@example.org) with numerous contributions by others.
A particular kind of music/dance (and some would say lifestyle) native to,
but no longer restricted to, a small region of Andalucia in Southern Spain.
Like American "blues" it probably has ancient antecedents, but as a distinct
genre is only a couple centuries old. Not all Andalucian folk music is
flamenco. Not all flamenco artists have been Andalucians (eg Sabicas), or
even Spanish (eg Greco).
Some classical guitarists (understandably, if they haven't studied flamenco)
view flamenco as a "style" of guitar playing emphasizing certain techniques
above others and having a distinct sound. Thus (oversimplified) if you play
rhythmic rasqueados and fool around with Phyrygian scales and a lot of
Ami>G>F>E, it's flamenco. Not so. At most, flamenco-ish.
Flamencos themselves (ie guitarists, dancers, singers, aficionados),
whatever their own specialty, and for both formal and historical reasons,
usually agree that what is fundamental to flamenco is *cante* (song), i.e. a
body of several dozen forms (*palos*) with specific rhythms, melodies, and in
some cases themes, sung in a certain way.
Flamenco guitar started as accompaniment for cante, and in Spain has largely
remained that, no matter how technically refined it has become. Probably the
same is true of flamenco dance -- that it started as an embellishment through
movement of what the singer was doing. Even the virtuosos like Paco de Lucia
and the late Sabicas who are famous for solo work (and who play other music
besides flamenco) would probably define flamenco in terms of cante rather
than of guitar technique. Both started within the tradition as accompanists
of cante, and were superb ones. To anyone familiar with cante, even their
solos imply the cante from which they came.
Spaniards know this already. You say "flamenco" and they think "Camaron"
(a popular singer who died in 1992) or "solea" (a song form) -- whether they
like the stuff or not. Non-Spaniards rarely hear cante, and understandably
have different associations -- for instance, the guitar played in a
particular way. So it's important to emphasize for them that cante is
central to flamenco in a way that a particular rasqueado isn't.