Latin jazz is the general term given to jazz with Latin American rhythms.

The three main categories of Latin Jazz are Brazilian, Cuban and Puerto Rican:

1. Brazilian Latin Jazz includes bossa nova
2. Afro-Cuban jazz is a fusion between Cuban music and American jazz
3. Puerto Rican jazz is a concept made by William Cepeda that celebrates Puerto Rico's heritage and African roots with a new shade of jazz and hip flavor

 - Text from: Wikipedia-Latin Jazz

History

One of the contributions of Latins (Latinos in Spanish) to America, Latin jazz gained popularity in the late 1940s. Arguably the first Latin-influenced jazz song is Caravan, written by Juan Tizol and first performed in 1936.

Dizzy Gillespie and Stan Kenton began to combine the rhythm section and structure of Afro-Cuban music, exemplified by Machito and His Afro-Cubans, whose musical director Mario Bauza created the first Latin jazz composition "Tanga" on May 31, 1943, with jazz instruments and solo improvisational ideas. "Tanga" was the first jazz composition based on the clave rhythm. Bauza developed the 3-2/2-3 clave terminology and concept, which is a staple of contemporary Latin jazz and salsa music.

On March 31, 1946, Stan Kenton recorded "Machito", written by his collaborator / arranger Pete Rugolo, which is considered by many to be the first Latin jazz recording by American jazz musicians. The Kenton band was augmented by Ivan Lopez on bongos and Eugenio Reyes on maracas. Later, on December 6 of the same year, Stan Kenton recorded an arrangement of the Afro-Cuban tune The Peanut Vendor with members of Machito's rhythm section.

In September 1947, Dizzy Gillespie collaborated with Machito conga player Chano Pozo to perform the "Afro-Cuban Drums Suite" at Carnegie Hall. This was the first concert to feature an American band playing Afro-Cuban jazz and Pozo remained in Gillespie's orchestra to produce "Cubana Be, Cubana Bop" among others.

 - Text from: Wikipedia-Latin Jazz

Differences with traditional jazz

In comparison with traditional jazz, Latin jazz employs straight rhythm, rather than swung rhythm. Latin jazz rarely employs a backbeat, using a form of the clave instead. The conga, timbale, güiro, and claves are percussion instruments which often contribute to a "Latin" sound. - Text from: Wikipedia-Latin Jazz

Sub-types of Latin jazz

Samba originated from nineteenth century Afro-Brazilian music such as the Lundu. It employs a modified form of the clave. Bossa Nova is a hybrid form based on the samba rhythm, but influenced by European and American music from Debussy to US jazz. Bossa Nova originated in the 1950s, largely from the efforts of Brazilians Antonio Carlos Jobim and João Gilberto, and American Stan Getz. Its most famous song is arguably The Girl from Ipanema sung by Gilberto and his wife, Astrud Gilberto. - Text from: Wikipedia-Latin Jazz

Playing style

Latin jazz music, like most types of jazz music, can be played in small or large groups. Small groups, or combos, often use the bebop format made popular in the 1950s in America, where the musicians play a standard melody, many of the musicians play an improvised solo, and then everyone plays the melody again. In Latin jazz bands, percussion often takes a center stage during a solo, and a conga or timbale can add a melodic line to any performance. - Text from: Wikipedia-Latin Jazz

Afro-Rican jazz

Afro-Rican jazz is an original concept developed by trombonist, composer/ arranger William Cepeda that celebrates the heritage of Puerto Rican music and its African roots while creating a new shade of jazz with a hip flavor. Steeped in the jazz tradition (having studied and performed with Dizzy Gillespie, Lester Bowie, Jimmy Heath, Slide Hampton, David Murray and Donald Byrd among others), Cepeda developed this unique artistic expression by incorporating a contemporary jazz perspective with the musical and cultural traditions of his homeland, Puerto Rico.

There are also other Puerto Rican musicians such as Papo Vazquez considered one of the pioneers of Afro Puerto Rican Jazz along with Cortijo, Edgardo Miranda, David Sanchez and others. Please update this info it will be much appreciated. - Text from: Wikipedia-Latin Jazz