The Mambo is a rhythm dance of Afro-Cuban origin; it was popularized in the United States in the 1950's by the famous bandleader Perez Prado. Mambo is a rhythm dance that does not progress along the L.O.D., and is characterized by Latin hip movement, breaks, and "shine" or "challenge" movements in apart position.
The Mambo was also the precursor to (and eventually eclipsed by,) the more popular Cha-Cha, which inherited the playful, flirtatious character of the dance along with it's characteristic breaks and challenge movements.
In it's original form, this dance was often done in groups as "Mambo Lines", as well as in circle, with partners progressing from one to the next; this almost-lost art is one of the most exciting and unique aspects of the Mambo, and is currently showing signs of revival in some places.
There is considerable controversy about the timing of the Mambo. Conventional school figure technique requires the dancer to hold the one beat and break (rock step,) on the second beat of the measure; this is how the figures have been presented in the charts, is expected in competition, and, according to the dance establishment, is the authentic timing of the dance.
Many dancers find this timing difficult, but it's a major characteristic of the dance. Watch the films "Dance With Me" and "The Mambo Kings" for good examples of this rhythm.
In social situations, a trained dancer who is accustomed to breaking on two would be well advised to be particularly sensitive to the skills of their partner; if, as is often the case, the partner seems determined to break on the one, then it is better to forego the "correct" break in favor of considerate partnership.