From 1919 to 1927, Breakaway was a popular swing dance developed from the Texas Tommy and Charleston in Harlem's African American communities. The Breakaway was danced to jazz, and while it often began in closed position, the leader would occasionally swing the follower out into an open position, hence "Breaking away".
When in open position the dancers would improvise with fancy moves. Some variations included both dancers completely breaking away from each other to dance 'alone'.
George Snowden is popularly credited with bringing the Breakaway to the mainstream after participating in a 1920s New York City dance competition, although it is difficult to be sure he was the only dancer of the day performing the step. Footage of Snowden dancing the Breakaway can be seen in the 1929 short film After Seben (directed by S.J.Kaufman).
Norma Miller credits "Twist Mouth" George with having pioneered the breakaway (or at least bringing it to the streets of Harlem) in her book "Stompin' at the Savoy."
It is this 'breaking away' which revolutionised the then current European partner dancing structure. For instance in the Polka a step called the Coquette (Love Chase)is defined as "The lady escapes from her partner and polkas solo while the gent pursues her, arms akimbo." By the late 1920s, Breakaway had been incorporated into Lindy Hop, which replaced it as a popular social dance.
19th century POLKA variations http://socialdance.stanford.edu/syllabi/polka.htm