Just to give a user-friendly summary:
It is made up of "day" and "night" cycles which take 24+ hours each. At night, anyone with actions uses them by PMing the host, during the day we all discuss and vote who we want to "lynch". Whoever is lynched dies and is removed from the game, and we find out their role. Anyone who is killed at night (by whoever has the kill power), their role is NOT revealed (but they are removed from the game.) People have roles such as save a player, spy a players role, sometimes there is block a players action. Other people are "vanilla townies" and do not have a night action, but get to vote during the "day" cycle.
The baddies know who each other are and can discuss and strategise privately behind the scenes. The goodies only know their own role and don't know who the other goodies are. During the day, goodies AND baddies converse on the forum, all pretending to be goodies, and trying to put blame on each other while deciding who to vote out.
It is a game of trickery and deception but also of logic. By reading the day and night posts (made by the host, saying what actions were done on who), you can eliminate people as being certain roles. Also, when we are voting to lynch someone, people who are close to being lynched will come up with defences which can give intended and unintended information. The goodies win if all the baddies are dead and the baddies win if all the goodies are dead. That is a summary of the basic way to play it.
As for time investment, at a minimum you should log on once a day and post but preferably a few posts or more a day. Over the "night" period (which covers a real time day and night, or sometimes longer), you only need to PM your action to the host. Depending on the game, sometimes there is posting during the "night" cycle and sometimes not.
In my signature is the link to the Newbies guide to Mafia, also linked by Hirkala and also stickied on the games forum.
P.S - It is very addicting!