An ex-con is a person who was in prison for a crime and is now free. It is informal. Newspapers and crime stories use it a lot; though actually, in some mouths it sounds rough, as if the prison years are still the main thing about the person. A kinder or more careful way is former prisoner or ex-convict. Con here is short for convict. It is not the con in con artist, which means a trick — that is a different word that just looks the same.