If someone is said to be allegedly guilty of something, it means that proof has yet to be produced or they have yet to be found formally guilty by law.
Allegedly is used almost entirely in a legal sense, referring to a potentially criminal action that is being or will shortly be decided in court. (It's from the medieval English word allege, meaning "quoted" or "brought forth in court.") For less serious matters, such as whether or not your boyfriend called you a liar, the word supposedly is generally used. Though watch out, because if you take him to court, you will become "allegedly a liar."