This is actually a 1958 album titled Machito With Flute to Boot with one substitution: track 1 on this album replaces a track on that one titled Davis Cup.
The music is pure Afro-Cuban. The sound samples will treat you to a quick run trough of the music and if you listen carefully you may pick up more than Herbie Mann. Aside from Machito's entire backing ensemble (including Machito himself and some of his stars like Rene Hernandez on piano and percussion, and Mario Bauza on trumpet) there are some jazz stars too. The tenor sax is none other than Johnny Griffin, and Curtis Fuller is on trombone. The baritone sax is Leslie Livrament about whom I know practically nothing.
All of the tracks, except the first one, are Herbie Mann compositions, so this album will provide insights into his amazing skills as a writer as well as a musician. Machito's backing band (and the other musicians named above) are perfect for each composition. Mann can run from blazing hot to laid back and cool and everything in between. This album showcases his range.
Three fourths of this album is also on a compilation titled Essential Jazz Masters that I recommend checking out if you like the sound samples on this page. On that compilation the tracks from this album are 3, 5, 8, 19, 20, 28, 34 and 40.