Answer by taking a quote from the following article:

The Beatles were an English rock band formed in Liverpool in 1960. With members John Lennon, Paul McCartney, George Harrison and Ringo Starr, they became widely regarded as the foremost and most influential music band. Rooted in skiffle, beat and 1950s rock and roll, the Beatles later experimented with several musical styles, ranging from pop ballads and Indian music to psychedelia and hard rock, often incorporating classical elements and unconventional recording techniques in innovative ways. In 1963 their enormous popularity first emerged as "Beatlemania"; as the group's music grew in sophistication, led by primary songwriters Lennon and McCartney, the band were integral to pop music's evolution into an art form and to the development of the counterculture of the 1960s.

Touring internationally in June and July, the Beatles staged 37 shows over 27 days in Denmark, the Netherlands, Hong Kong, Australia and New Zealand. In August and September they returned to the US, with a 30-concert tour of 23 cities. Generating intense interest once again, the month-long tour attracted between 10,000 and 20,000 fans to each 30-minute performance in cities from San Francisco to New York.  In August, journalist Al Aronowitz arranged for the Beatles to meet Bob Dylan. Visiting the band in their New York hotel suite, Dylan introduced them to cannabis. Gould points out the musical and cultural significance of this meeting, before which the musicians' respective fanbases were "perceived as inhabiting two separate subcultural worlds": Dylan's audience of "college kids with artistic or intellectual leanings, a dawning political and social idealism, and a mildly bohemian style" contrasted with their fans, "veritable 'teenyboppers' - kids in high school or grade school whose lives were totally wrapped up in the commercialised popular culture of television, radio, pop records, fan magazines, and teen fashion. To many of Dylan's followers in the folk music scene, the Beatles were seen as idolaters, not idealists." Within six months of the meeting, according to Gould, "Lennon would be making records on which he openly imitated Dylan's nasal drone, brittle strum, and introspective vocal persona"; and six months after that, Dylan began performing with a backing band and electric instrumentation, and "dressed in the height of Mod fashion". As a result, Gould continues, the traditional division between folk and rock enthusiasts "nearly evaporated", as the Beatles' fans began to mature in their outlook and Dylan's audience embraced the new, youth-driven pop culture.  During the 1964 US tour, the group were confronted with the reality of racial segregation in the country at the time, particularly in the South. When informed that the 11 September show at the Gator Bowl in Jacksonville, Florida was to be held at a segregated venue, the Beatles expressed astonishment and announced that they would refuse to perform unless the show become integrated. Lennon stated: "We never play to segregated audiences and we aren't going to start now ... I'd sooner lose our appearance money." The group's stand drew controversy in the local media, but city officials relented and agreed to allow an integrated show. On the tour the group also refused to stay in segregated hotels. Documents reveal that for their subsequent US tours in 1965 and 1966, the Beatles included clauses in contracts stipulating that shows be integrated.

When did they meet Bob Dylan?
In August, journalist Al Aronowitz arranged for the Beatles to meet Bob Dylan.