John Lennon, a neighborhood guitar-player (local trouble-maker, part-time shoplifter and full-time egomaniac) had been playing around at a few local gigs in the area for a year or so. John’s initial band was called “The Blackjacks”, consisting of a few of his mates from school. Soon thereafter, the band’s name was changed to “The Quarrymen”, in honor of their present school, Quarry Bank High School.
Paul had been invited to watch the Quarrymen by a mutual friend. After the band’s first concert, Paul was introduced to John... After the brief introduction, Paul played John the song “Twenty Flight Rock” by Eddie Cochrane. John decided to “make the group stronger” and asked Paul to join.
Paul kept the songs neatly arranged in a notebook and each new tune was listed as “Another Lennon-McCartney Original”. The two made a lifelong pact to continue composing in this way and earnestly shook on it. (This handshake was the only actual songwriting agreement the two had; they never signed a written contract as inevitable co-composers.)
Although both John and Paul continued to compose songs on their own too, they never broke their pact and every song, whether solo or co-written, was given the “Lennon-McCartney” label.
Today I Found Out has links and more detail, plus these related posts: