John Lennon and Paul McCartney wrote this as a showcase song for George Harrison, who sang lead. George had already written only one Beatles song by this point: "Don't Bother Me." (thanks, Adrian - Wilmington, DE)
Typical of the early Beatles, this is a very innocent song - the singer is taking it slow, as he's OK just dancing with the girl of his dreams. There is an old-time Irving Berlin/Cole Porter feel to the song, focusing on the de-lightful feeling of being smitten.
The Beatles performed this in their movie A Hard Day's Night, giving Harrison some quality screen time.
John Lennon wrote most of this song. Typical of his style, the first short notes are followed with tree longer notes. The Irvin Berlin influence comes when the melody rises in the five notes in "kiss or hold your hand..." In the cadence, Lennon jokes: he repeats the mentioned five notes, but just sinks it with a third. (thanks to Johan Cavalli, who is a music historian in Stockholm)
The Beatles recorded this on Sunday, March 1, 1964 in 4 takes. Recording on a Sunday was very rare at the time. (thanks, Ben - Cheverly, MD)