"Parents Strongly Cautioned. Some material may be inappropriate for children under 13. This signifies that the film rated may be inappropriate for pre-teens. Parents should be especially careful about letting their younger children attend. Rough or persistent violence is absent; sexually-oriented nudity is generally absent; some scenes of drug use may be seen; one use of the harsher sexually derived words may be heard."
The PG-13 rating exists for films that are considered too adult for the PG rating, and yet not so mature as to warrant an R (Restricted) rating. The rating is a meant as a warning to parents before allowing their pre-teen children to see a film. And unlike R, it doesn't prohibit anyone from seeing the film - children under 13 should still be admitted to PG-13 movies no questions asked. The PG-13 rating, and in fact all ratings exist solely for parents as a guide to determining which movies they want their kids to watch. If parents want to restrict all films based on the MPAA ratings, it's their own decision.
The reason that the PG-13 rating came about was because the Classification and Review Administration, a group of parents who rate films for the MPAA, had difficulty classifying films between just two ratings: PG and R. There were several films that were probably suitable for people under 17, but were rated R, and films that weren't suitable for pre-teens, but were being rated PG.
Take for example "The World Is Not Enough" (Rated PG-13). James Bond movies are filled with sexual innuendo and cartoonish violence (although people DO get shot). You'd have a hard time explaining why it should be rated R, though. But on the other hand, it's not the kind of movie you'd take the average eight-year-old to. But before 1984, those were the choices. Rate it R, and keep anyone under 17 from seeing it without a parent (or a drunken wino who you paid ten bucks), or rate it PG, and mislead parents into believing that the content in the film is suitable for children.
Thus, the PG-13 rating was born. It started with Red Dawn, and it continues today. And it's a good thing. A guide. Not an oppressive tool of The Man.