This was the first single from DJ Jazzy Jeff & the Fresh Prince, who made quirky, easily understood rap that enjoyed mass appeal, especially with kids. What's surprising about "Girls Ain't Nothing But Trouble" is that it's about a false rape accusation.
In the song, Smith wines and dines a young lady who then screams rape, takes his wallet and runs. The cops show up and arrest him for aggravated assault. It seems shocking that this was played for comedy, but the song was so clearly novelty that it escaped scrutiny.
The rest of the song is more conventional: The next verse finds him at a girl's place when her boyfriend walks in on them, forcing him to escape out the window in his underwear. Finally, he shows up to take a girl on a date, but she takes so long to get ready that he falls asleep.
The duo released a similar song (with another very literal title) on their next album called "Parents Just Don't Understand." That one took off, getting steady airplay on MTV and earning Smith his own TV series, The Fresh Prince of Bel-Air. Smith was 21 by the time the show went on the air in 1990, but he played young: by rapping about girl trouble and annoying parents, he embodied hip-hop for many kids who were not exposed to the culture.
The video was directed by Scott Kalvert, who did the 1995 movie The Basketball Diaries. Kalvert developed a distinctive look for the video, using colorful graffiti, outlandish costumes and props, and manic sequences shot with a fisheye lens. This style became the template for future DJ Jazzy Jeff & the Fresh Prince videos, including "Parents Just Don't Understand," and it was also used as the look for the opening sequence of The Fresh Prince of Bel-Air, which Kalvert directed.
This samples the theme song to the sitcom I Dream of Jeannie, adding to the overall levity.
This was released in 1986 on an independent Philadelphia label called Word Records, which was later re-named Word-Up Records. It didn't chart in America, but got the attention of the major label Jive, home to early hip-hop acts Whodini and Kool Moe Dee, which signed the duo and issued their first album, Rock the House, in 1987. After their second album, He's the DJ, I'm the Rapper, took off in 1988, Jive re-issued "Girls Ain't Nothing But Trouble" as a single. This time it reached #57.
In the UK, the song was released the first time around on the Champion label, and reached #21. So yes, the UK was about two years ahead of America on DJ Jazzy Jeff & the Fresh Prince.