A subgenre of jazz typically played by groups of 3 to 5 musicians ("combos") and typically charactarized by radically altered chords and phrases, wildly creative improvisational flights, great complexity, and a sound that can be intimidating to unfamiliar ears.
By the early 1940s, those who had come of age during a time when jazz had been immensely popular were beginning to come into their own as musicians; in the typical fashion of 20th century art, they took what they were familiar with and greatly expanded its scope, depth, and intensity. In a gradual development that took place mostly on small club stages, swing in the hands of geniuses like Charlie Parker and Dizzy Gillespie became Bop.
Of course, the development didn't seem gradual to the public, mostly because the years of bebop's inception were those of World War II, a time during which a recording ban had been instituted to conserve scarce resources (update: someone told me this was wrong; disregard it). A few Cats heard the music throughout its development, but everyone else encountered it suddenly in 1945, and while it spread like wildfire among musicians (who played it to the exclusion of almost all previous jazz), for many others the leap was too great -- the unfamiliar harmonies seemed dissonant, the unfamiliar rhythms tense and jittery.
It was the beginning of the end for jazz in the United States. Through the 1950s and '60s the genre continued on the path bebop had set, becoming more and more incomprehensible to most people, who were listening to Jimi Hendrix and the Beatles. Today, only 4% of all records sold in the U.S. are jazz, and many large cities (Washington, D.C., for example) have not a single station on the dial that plays it (though I'm proud to report that my town has 2 -- WEMU and WCBN). In Europe (and Japan), however, Jazz has remained popular, and thousands gather yearly for summer jazz festivals in cities around the continent, listening to largely American musicians play largely American music.