Jazz music first appeared sometime in the 1890's. It is typically thought to have originated in New Orleans.
This is not strictly true.
Music in New Orleans is well documented, but much of the same things were happening in American south, southwest, mid-west, and even in California.
One reason to use New Orleans as the primary spot is because of the documentation that exists about its music and early practitioners.

Some of the elements of Jazz originated in African music. The African languages rely on the way in which phrases or words are said as much as on the word itself.
So for musicians they are trying to attempt to speak the human voice with their instruments.
So since African Americans are located all over the world how could historians say that it just started in New Orleans?

Another point of why Jazz is said to originate in New Orleans is because of the Mississippi river opening at the mouth of New Orleans.
Many of the shipments came through the harbor and that brought much entertainment.
So different styles of music began to pick up such as ragtime and swing.