Cultural motivations for interest in these musics include the emergence of independent African nations, beginning in the late 50's; black Americans embracing their African heritage and studying all aspects of African cultures, and the increasing interest in Indian philosophy/religion in Western cultures.
Musically, as artists moved from European harmonic ideas into modal forms, they found cultures with well-developed systems of modal music (particularly, of course, in Indian music, which is structured around thousands of identified ragas, which are roughly comparable to modes.)
While Art Blakey is recognized as the first major jazz musician to have traveled to Africa to study, his application of African musical elements to his music was limited. Artists like John Coltrane and Yusef Lateef made more committed efforts to integrate sounds of Africa and India into their music. Trumpeter Don Cherry is often considered the "father of world music" for his wide-ranging studies of musical styles and instruments.
For extensive information about jazz fusions with Indian music, see the excellent Guide to Indian Classical/Jazz Fusion by Allen Lutins. Anyone interested in developing a comparable resource for African/Jazz fusions, information about the excellent jazz musicians who have emerged from Africa, or other related information, please contact me at j-germuska@nwu.edu.