This is the title of a song by Charlie Parker. So the first joke in the title is the reference to Parker's nickname, "Bird."
The second joke is the intellectuality of bebop. Bebop musicians adopted a self-consciously intellectual pose, and were fond of polysyllabic words. It's a joke because it is a bit jocular in tone, and part of the public face of the movement, as reflected in media portrayals. Of course, they were intellectuals in their approach to musical complexity, so the jocular persona did in fact correspond to something genuine. The beatnik fan of the music also saw him or herself as smart in this way. There are other song titles that do this like "Anthropology," or "Epistrophy."
Polysyllabic words and titles also have an onomatopoetic value, referring to the fast phrases consisting of many notes.
The song itself is a contrafactum of "How High the Moon." It uses the same chords. A new composition on old chords: making it new. This requires a new title as well.