Here's a link to a vintage video of Johnny Otis' 1958 hit song "Willie And The Handjive"

http://www.youtube.com/watch?v=b9Bqf_IxGJU&feature=related

-snip-

In the context of that song, "doin that crazy handjive" is a
Rock n' Roll dance or at least some hand motions that is done while dancing to Rock n' Roll music. The implication in the song is that the person doing "the handjive" is "cool" or "hip" (these being two other vernacular terms that have, for the most part, are no longer used by African Americans and other people who stay up to date with the latest slang words & sayings).