Mas o menos it's about Charlie Brown and his struggle to fit in. Each character has their own story going. Which is why the "Happiness" song in the end is cruial.
Charlie Brown is self-consious and a little kid in love. With the help of his friend Lucy, he feels as though no one, even his sister and dog, like him. He tries hard to suceed but always feels like a failure. Sad for such a little kid.
Sally Brown is fiesty and doens't have an essential problem. Little things charge her temper like ice cream falling or jump ropes. But she's a fun lovng kid and she's one of the best characters, IMHO
Snoopy is the dog of the Browns. He basically wishes he were a human. He loves adventurous stories and playtime. Throughout the musical, he's the sarcastic character, showing his joy and yet dismany of being a dog. To quote, "Today I am a dog. Yesterday I was a dog. Tomarrow, I'll probably still be a dog. There's just so little hope in advancement."
Schreoder is a musical genius who just wants to play the piano and spread the joy of music. A simple and yet good character, he prefers playing music than appreciting the love showered upon him by Lucy.
Lucy is a stubborn, sometimes cruel character. She makes other people, especially Charlie, feel badly..and charges for it. She's sort of the Angelica from Rugrats of the story.
And Linus. A simple child who wants to part from his baby ways of carrying around his blanket but can't seem to. His genius at academics isn't praised the way it should be, and he tried getting along with his older sister Lucy. A hard task.
All of them share common woes like school and simple joy. But it's a great, cute story with great music and great characters.
Hope this helps
"It's a great feeling of power to be naked in front of people. We're happy to watch actual incredible graphic violence and gore, but as soon as somebody's naked it seems like the public goes a bit bananas about the whole thing."