Classic Style (not “classical”) banjo is a fingerpicking style that rose to popularity in the late 19th and early 20th century, as minstrelsy waned and the banjo became a more respectable parlor instrument. It’s a finger-picked style, played on fretted banjos without fingerpicks. Modern players often use nylon strings, but banjos of the period would have been strung with gut strings.
The repertoire reflected the popular music of the time, featuring many fine marches, cakewalks and rags. It’s an elegant and very evocative style, quite different from the old-time, bluegrass and country traditions that succeeded it.