"jam session. 1. Orig. Jazz an informal and typicaly impromptu session of jazz music; (broadly) an informal meeting of musicians to play for enjoyment.

1933 Fortune (Aug.) 90: Not unlike the jazz musicians jam sessions where the players vie with one another in hot solos. 1936 Harper's (Apr.) 574: Thus in a typical "jam session" one instrument will lead off with a slightly modified form of the general melody, the other instruments "faking" the harmony.
1936 Benny Goodman and His Orchestra Jam Session [Victor phonograph record VIC 25497].

From the word "jam n. 1. Esp. N. E. a large social gathering or party.
1827 H. W. Longfellow, in DAE: I have been several times to her evening jams but as it was Lent, there was no dancing.
And so on....
1929 Perelman... She did not know Paul Whiteman personally ..... So one night she went to a jam and met ...Izzy Worknan."
1929 OED2: There are many variations on this rhythm...which make excellent breaks- or "jams" as they now call them when they are taken by the whole band."


From J. E. Lighter, Historical Dictionary of American Slang Vol. 2, p. 246; 250. Random House.