Torn things have been pulled apart or ripped. Things can be literally torn, like a torn piece of paper, or figuratively torn — like your torn heart when you have to take sides in a family feud.
You can serve a salad full of torn lettuce leaves, or mend a stuffed animal with a torn ear. In both cases, something has been divided by force, or pulled apart. It's also possible to be emotionally torn, or conflicted between two choices, options, or people: "I'm torn between going to the party or staying home and reading my library book." Either way, torn things are difficult (and sometimes impossible) to repair.