A claim or statement that is alleged hasn't been proven true — if you're an alleged murderer, you've been accused but not convicted.
When a fact is alleged, there is doubt about its accuracy. The word alleged is often used in connection with court cases, because the accused is innocent until proven guilty: an alleged robber is a suspected robber but has not been proven guilty of robbery. Journalists often use alleged in news stories when someone’s guilt is suspected but not confirmed. Sometimes alleged means doubtful or dubious, as in "Who is this alleged expert?"