Back several generations in the south there used to be "road houses", which were somewhat similar to nightclubs today, but much more wide-open in terms of the activities that took place in them. They were also sometimes known as "honky-tonks", and so the music that was played in them was naturally named after the establishment. Many of the early ragtime and jazz pianists got their start in road houses playing for dancing and for atmosphere. Out of honky tonk - or at least contemporary with it - came boogie woogie, blues, and jazz. Perhaps the closest thing to that style of playing today would be Jerry Lee Lewis.
Honky-tonk piano is a very rhythmic, very rollicking style of piano playing most often associated with ragtime. The term itself comes from a name given to certain bars in the early 20th century; these were rough bars that often encouraged rowdy behavior and brought in self-made piano players to entertain the roughshod crowd. When honky-tonk piano first emerged, it seemed to be a musical representation of that type of behavior; honky-tonk piano was rowdy and rough, catering to working-class audiences who just wanted to dance and have a good time.
The honky-tonk piano style itself is extremely distinctive, enough so that a particular sound associated with it is included on modern digital keyboards. It's a slightly out-of-tune, twangy sound that reflects an old piano being played in an old bar. It's similar to ragtime; but unlike ragtime, honky-tonk piano is less concerned with overt melody and more with the percussive elements of the player. It was extremely rhythmic, extremely danceable and extremely popular among ragtime fans. And what's more, honky-tonk piano eventually went on to inspire a whole host of piano styles, including some branches of jazz and boogie-woogie; in some ways, the original honky-tonk piano was a precursor to the familiar walking bass found in a variety of musical styles.
Honky-tonk piano has since morphed into a style different from that of ragtime, a style sometimes associated with backwoods country music. It could have something to do with the honky-tonk piano's specific sound; the out-of-tune honky-tonk piano tone at times mimics the quality of instruments like banjos and fiddles, creating a great complement to the fast, vivacious music found on the front porches of southern homes. And honky-tonk piano even moved forward to influence many branches of modern country music, especially alternative country that relies heavily on rhythmic elements as opposed to melodic.
