Although the origin of the word ragtime is unknown, many believe that it originated from the words 'ragged time' refering to the characteristic syncopations which 'tear up' the then normal accentuations of previous popular music.
Another belief is that these words are associated with the walking bass set against the melodic line. Yet another belief is that since the ragtime was dance music, then dancers would have to roll up the rug or 'rag' to use the hard floor in order to dance in this particular fashion.
The last theory, my favorite, is that the ragtime was the type of music that one would fine in saloon bars where the prostitutes were not available, because they were 'on the rag.' Thus the name 'rag' time.
Ragtime is a distinctly American musical style. It may be considered a synthesis of African-American syncopation and European classical music.
If you would like to listen to some ragtime music please follow this website
http://www.trachtman.org/ragtime/