Mafia is a forum based game where there are 2 main sides. Players are assigned roles in a village based on different themes (Star Wars, LOTR and so on), there is the mafia trying to kill all of the villagers, and the villagers trying to kill all of the mafia, sometimes there is a lone human trying to kill both sides (If I recall). A thread will be made and both sides will be making reads (trying to analyze past posts to see if someone is mafia or not) on other players. The mafia during this time try to misdirect while the villagers need to pick who to trust. There will be 2 phases, day where everyone talks in a big thread and discusses who is most likely mafia, at the end of the day people vote on someone that they will hang for that day. At night the mafia gets to work in their own secret thread, they decide how they want to operate the next day and have their own time to kill someone. Night is also the time when special features activate, some villagers have no features, the mafia all have a feature, and some villagers do have a feature. That feature might be to roleblock (They can perform their role), kill someone, or prevent someone from being killed.
I think that is a decent enough summary. The first page in this thread links to previous games and a more indepth description.