Your reputation is unsullied, or unsoiled, because you study hard, you don’t skip school, and you are generally kind to everyone. Your friend’s reputation hasn’t stayed unsullied since he got caught selling answers to tests.
To understand the adjective unsullied, you must understand its root, sully, "to soil or tarnish." Something unsullied is spotless: you usually refer to things in the abstract in this way — your military record may be unsullied by disciplinary actions, your report card may be unsullied by grades lower than A.