"Day" is a role modifier that signifies that the effect of the role happens during the Day. It is only used for roles that would otherwise be understood to take effect at Night. These abilities tend to resolve as soon as the moderator gets the action submission. Depending on the text of the ability, players may have to post that they want to use their ability inthread, or may have the option of sending in their action via PM.
The most common example is Day Vigilante, or Dayvig. This is a Vigilante who can kill a player on command during the Day. Very rarely, DayCops may appear; and in games with kills that resolve during the Day, Day Doctors have also been heard of.
Mixing Day actions and Night actions, especially with regard to protections and roleblocks, can lead to some confusingly-worded roles. More often, Day abilities are considered "outside" Night action resolution - therefore, Roleblocking a Dayvig overNight would be meaningless since the Dayvig doesn't shoot at Night.
As a result, the Day modifier tends to decrease the swing of a role (since it is more likely to go through) while greatly increasing its power (since its effect occurs during the Day while the Town is around to talk about it).
As an aside, because of the style points and immediate nature of Day roles, they are often faked as a joke or to garner reactions. This is especially true of daykills, which are common enough that players are not necessarily sure whether a claimed daykill was faked or not.