How Prominent Is Improvisation In Jazz Music?

What makes jazz a distinctive art form is not so much its dissonance or its syncopation as the element of improvisation. Yet here, too, improvisation in the form of a theme with variations has long been an art form. But in jazz it is not worked out ahead of time as in 'serious' music; it is all done impromptu, spontaneously. The jazz musician, therefore, depends upon his knowledge of the harmonic structure of the original theme and a highly developed ear in order to produce spontaneously his improvisations.
But some have gone too far, just as mentioned earlier in connection with serious contemporary music. There has come into existence that which is known as "Free Jazz." Here there are no rules, no acceptance of anything traditional, a rejection of the chordal system that has marked beautiful music of the past. This has resulted in a sort of rebellion against all known musical theory and harmony. Not only are the musically uneducated repulsed by the disorganized screeches emanating from wind instruments and other hit-and-miss attempts at something worth while, but many serious jazz musicians cannot accept these new extremes in the interest of music. It definitely is not 'the organization of sound toward beauty.

I cant believe you denied my answer. JImmi hendrex was the man.
Ok how bout joe satrani. He improvises all his solos. His music is rock experimental jazz. It depends on the song.   

Ne how it is very important because the musician improvises a sole and records it and learns it and now can compose a piece around the improvision and  call it a Steve Vai song....