It was a big deal for John Lennon and Paul McCartney to use the phrase "Turn Me On" in the lyrics. It was a drug reference. Years later, they would use the line "I'd love to turn you on" in " A Day In The Life."
The woman in the title apparently gets the singer high on marijuana. This is the first time The Beatles used a direct reference to pot in a song. Bob Dylan introduced the band to marijuana when they met on August 28, 1964 in a New York City hotel. Dylan was surprised The Beatles hadn't tried it before, as he thought the line "I Can't Hide" in " I Want To Hold Your Hand" was "I get high." (thanks, Bertrand - Paris, France)
Written and recorded the same day, this song was used as the B side of "I Feel Fine."
McCartney has acknowledged Little Richard as big influence, which is apparent on his vocals for this song.
A chocalho, which is a type of metal shaker, was used for percussion.
In 1965, a Tex-Mex group called the Sir Douglas Quintet released a song called "She's About A Mover" which was a direct rip-off of this. That song hit #13 in the US.
The British new wave pop band Scritti Politti recorded a cover with Shabba Ranks, which peaked at #20 on the UK singles charts in 1991. Scritti Politti frontman Green Gartside recalled to Mojo magazine March 2011, the ragga star turned up at the studio, "mob-deep with guns, everything. His manager Clifton 'The Specalist' Dillon would physically get a hold of Shabba while Shabba was on the mike and thump him so he could feel the rhythm."