PG-13 was created about 15 years ago in reaction to a particular movie "Gremlins" which was pretty intense. It was rated PG, and a lot of parents took kids to it, then complained severly because the kids had nightmares, etc.
Basically, 13 is given as a general threshold that any 13 year old would be able to "handle" the movie. At least around us, the movie theater listings on the web-site give the ratings, and the reason for the ratings. In other words, it will say "Starship Troopers, rated PG-13 for mild violence, language, and brief nudity, showing at ....."
My kids are 9 and 11, and they've seen some PG-13 movies for the last few years. But there are some PG-13 movies that I still wouldn't let them see.
My take is that if it's PG-13, I make sure I understand what the story line is and why it's rated that way before we see the movie. If it's G, I assume it's appropriate for anyone. PG, I generally assume it's going to have one or two minor cuss words, so we'd go without too much worry.