When talking about
music,
trad was, in the UK at least, originally an abbreviation for 'traditional jass'.
Performed by such musicians as Humphrey Lyttleton and Acker Bilk, trad jazz was based around the New Orleans jazz of the 1920s, and much like the trad rock mentioned in Wagstaff's writeup was obsessed with recreating the music of a bygone age, down to original instrumentation.
Despite its obsession with recreating the past however, trad jazz actually paved the way for some of the most groundbreaking music of the 60s. Many of the bands would also perform folk and blues tunes from the same period as the jazz they played, seeing these as kindred forms. Lonnie Donnegan started out performing with these groups before going solo and only performing skiffle - starting the craze that led many young bands, including the Beatles, to form. (The Beatles' producer, George Martin, also worked with both Lyttleton and the Temperance Seven, and Lyttleton's Bad Penny Blues was a big influence on the Beatles).
Simillarly Alexis Korner got his start in Chris Barber's band, before going off to form his own blues band - which in turn featured most of the members of the Rolling Stones in the early stages of their careers.
It now seems ironic that this most regressive of musical forms should have such progressive results, but maybe it's necessary in music to go back to the beginning and strip away all the conventions that have grown up, before advancing again...