Theft is the act of stealing something. If you've ever taken your sister's sweater without asking her first, then she's right: that's an instance of theft!
The word theft refers to taking something from someone else without getting permission. Shoplifting is a form of theft, as is embezzling a million dollars from your business partner's Swiss bank account. In the United States, petty theft is the act of stealing anything worth less than $500, like someone's bike or a pack of gum. It's still a punishable crime, but you will get in much bigger trouble if you steal something more valuable, like a car.