It's been said that Cuba and New Orleans are more than musical cousins; they are more like twins and equally responsible for much of what we call jazz. And I've often heard New Orleans described by its multi-cultural natives as being not a Southern city, but a Caribbean city.
Cuba and New Orleans historically shared the same trade routes, and cultural exchanges and mutual musical influences have been traced dating back to the early 1800s.
In the nineteenth century, the Cuban contradance known as the habanera ("Havana-style dance") gained international popularity. In the US, probably the best-known example of the habanera style is from Bizet's opera Carmen:
http://youtu.be/OYfMRZTDLZQ
The first written music to be rhythmically based on an African motif, the habanera was a natural rhythm for the talented New Orleans musical community to incorporate into their works.
New Orleans musicians like Louis Armstrong and Professor Longhair used habanera rhythms in their compositions, and Jelly Roll Morton considered the habanera (which he called the "Spanish tinge") to be an essential ingredient of jazz.
You can still hear the Cuban habanera in the second-line of New Orleans brass bands and in the unique style of R&B produced in the Crescent City.
http://youtu.be/UBSN7WOPkQ0
Listen for habanera and more on Jazz Caliente, Thursday afternoons at 2pm on KPLU's Mid Day Jazz!