Today's jazz standards, also known informally as "The Great American Songbook" are a hybrid of several influences. (Note: the definition of which songs are "standards" varies by which musicologist you ask.)
I know of eight categories, but to answer your question I will group them into the four obvious categories:
1) African American musical styles: Blues and work songs evolved into what is now considered "traditional jazz," which category includes "Dixieland Jazz" (but in the northern towns like Chicago they call their version "traditional jazz"). This era was in it's prime from about the year 1900-1920. Today most of these songs are too archaic to be considered current standards, but they laid the groundwork for later composition.
2) Show Tunes and popular hits: Many great jazz composers got their start in composing popular music, especially in the high-stress music mills known as Tin Pan Alley in New York City. This region had been around for decades, but especially during 1920-1940 these small studios would crank out music for use in Broadway plays and elsewhere. From there they were scouted out by movie studios in Hollywood to create theme songs for films. Later, jazz players would borrow these songs for the basis of improvisations (a respected tradition in jazz).
3) Classical music influences: Jazz harmony, also known as "extended harmonies," were drawn from the innovations of the European "impressionist" composers (like Debussy). Iconic chord progressions were co-opted from the classics, like that from "Autumn Leaves" (Harpsichord Suite in G minor HMW 432, 4th movement). Pianist and bandleader Duke Ellington studied classical piano from an early age, learning all the classics and the "romantic" composers (i.e. Beethoven and Chopin). Both Louis Armstrong and Charlie Parker were known to practice melody lines from classical opera arias. These talented players, composers and improvisers were very much aware of music theory and classics.
4) The Latin-American influence: Since the boom Brazilian jazz in the 1950s, the styles of "bossa nova" and "samba" have been embraced in jazz standards. Also other afro-cuban styles and rhythms are commonly used.
Put all this together and you have the influences of The Great American Songbook (it's not actually a book, BTW, it's a concept). The only problem with defining jazz standards is that standards are what the jazz musicians play, and that varies by geographic region.