Days in Mafia are the phases between nights when all players are encouraged to discuss what has happened the previous nights and days, make accusations against other players, and cast votes to eliminate a player. Each day ends at a time determined and announced by the host, who publishes a day post.
While most actions are only used at night, there are still several actions that occur in both night and day (see: traps), while others yet are only of use during the days, mostly protecting a player from lynch (typically by RID) or modifying the vote count in some way.
Days are typically numbered in order and follow a similarly numbered night. Most games begin with a night, so the first cycle would be Night 1 to Day 1, followed by Night 2 to Day 2.
It should also be noted that game days and nights do not refer to any real-world time. Typically, nights and days are each 24 hours and are not dependent on any real-world time zone.