In its simplest form, Mafia consists of two sides: the Mafia, and the Town. The Mafia's goal is to kill the innocents, while the Town's goal is to kill the Mafia.
At the beginning of the game, the Moderator will secretly send everyone their role. The Mafia will know each other, while (in the basic game) everyone else will only know their own role.
The game has two phases, the first of which is Day. During Day, the Town must choose someone to Lynch; they are trying to eliminate the Mafia, but the Mafia can lead them astray by casting suspicion elsewhere. Generally, players will vote for someone they think is Mafia (the Mafia will vote so that they seem to be doing this as well, and might even vote for each other to confuse the Town); when a player gets a majority of the votes, they are lynched. Their role is revealed by the Moderator, and it becomes Night.
During the Night,no one can talk publicly. The Mafia, however, can speak to each other privately to plot strategy and decide who to murder before the next Day begins. At the end of the Night, the murder is carried out and another Day begins. In effect, the Town gets to kill someone, and then the Mafia gets to kill someone.
The game alternates between Day and Night until either the Mafia are eliminated, or the Mafia have killed everyone else (or nothing can prevent the same)

As in the Gmod Mod?