When something is forbidden, it's not allowed. You were forbidden to use your father's computer but you did it anyway — and that's why you're grounded.
You may recognize the phrase "forbidden fruit," which refers to a famous Bible story about Adam and Eve in the Garden of Eden. They ate an apple that God had forbidden them to eat, and there were terrible consequences. "Forbidden fruit" refers to something you want even more than you might otherwise, because you're not allowed to have it. If you know a little German, you may notice that forbidden sounds like its German equivalent, verboten.