A Day/Night Cycle is the normal passing of time that occurs when the player is in-game.
Fable, Fable: TLC, & Fable Anniversary[]
The clock visible on the top right corner of the minimap represents the current time of day. In the original Fable, every in-game day is 48 real-time minutes, whereas in Fable: The Lost Chapters and Fable Anniversary, every in-game day is 25 real-time minutes, effectively having a timescale of 57.6:1.
A Moonfish or Golden Carrot can be used to skip to either 9PM or 10AM respectively.

Clock Displaying 6:00 AM
Sleeping in a bed will result in the time being forwarded to 9PM (if you slept during the day) or 8AM (if you slept during the night).
Fable II[]
In Fable II the timescale is similar if not the same of Fable TLC around 60:1, but in this game sleeping in a bed will offer the choice of sleep for 6 hours, 12 hours, 24 hours or 7 days. Sleeping long periods of time can cause the Hero to gain weight, making them less attractive to others.
Some quests demand some actions to be executed at a certain period of the day, such as Donating to the Light, Sacrificing to the Shadows. The job Assassination Society often demand the victim to be killed at a certain time of the day.
NPC's will also have a more elaborate routine than the ones in previous games at certain times of the day, all having a wake-up and lay-down time which are announced by the Town Crier . Shops and stores will open and close at a similar pattern also announced by the Crier.
Fable III[]
In Fable III, a complete day-night cycle translates into about 20 real-world minutes. Shops are closed rather rigorously at night, with considerable consequences for the Hero careless of the fact. In other words, commercially-astute Heroes should plan their commercial or mercantile activity mindfully. To bypass the in-built cycle in the attainment of one's goals, the Hero can easily rest in any (legal) bed or resting-place and select the desired time of awakening.
The day/night cycle in Fable III is heavily incorporated into the (Legendary) weaponry of the game, where numerous weapons are enhanced and become capable of increased damage output if augmented appropriately, the reward of usage during the day or night, respectively (e.g., The Equaliser relic rifle does 40% more damage during the night in its "Nightowl" augment, similarly the uncommon pistol, Tee Killer Shooter, and accordingly the DLC swords, Shardborne and Wolfsbane; solar-wise, the special tool against the undead, the Bonesmasher pistol, the shop-grade Auroran pistol, Desert Fury, and the shop-grade rifle, Defender of the Faith, offer 30% more damage if relevantly augmented and utilized in the day.)