Watch the What is Bebop? online guitar lesson by Fareed Haque from Bebop Improv Survival Guide
Bebop is a style of jazz playing that developed in the early 1950s. Check out Charlie 'Bird' Parker, Dizzy Gillespie, Bud Powell. Early jazz musicians improvised by creating variations on a songs melody [ check out Louis Armsrong] , and later on improvised by building melodies thru arpeggiating or outlining the chords of a given tune [ check out Coleman Hawkins version of Body and Soul].
BeBop musicians took this a step further.
Not only did they play on the chords of a song, they had enough facility with arpegiating chords to arpeggiate more complex chords, and eventually began to add chords to the basic chord progressions, outlining substitute chords extra chords etc etc creating ever more complex and interesting melodic lines, often simply called "lines".
Another characteristic of the Bebop style is the increased use of chromatics to lead to and from chord tones, especially chromatics around 9ths, 11ths and 13ths [called 'Extensions'], and even altered 9ths, 11s or 13ths.