A day is defined by the turn. It begins with the first side's turn, and ends when the last side has it's turn. Due to the multitude of sides (at least ten+ introduced by name so far). The day does not seem to end until every side has used its turn. (It may be that turns are not continuous, that is, you may not hold up everyone else with your turn). Night seems to be a set time.
Alliances may put turns before people who previously had the first turn. They do this by breaking alliances and reforming them with others, who may have earlier turns. The day starts, then, with their turn.