Sleep can refer to two different things in the game, but both of them will have the same effect. With the exception of mechanical units and some creeps, many units are capable of sleeping, and many creeps will indeed sleep during the Day/Night Cycle.
 Sleep Ability
Dreadlords are heroes which have the ability to cast Sleep, an ability which will even cause heroes to lose consciousness. This is an ability which can only target one unit at a time, but can remove them from a battle for a prolonged period of time, a period which grows long as more skill points are put into the ability.
When sleeping, they cannot be woken until the time clock for the spell is over, and they cannot use abilities and fight back, although all passive defenses and bonuses will remain intact!
 Night Sleeping
While your own units will not do this, many creeps and in some campaign scenarios, units, will sleep during the night in the Day/Night Cycle. While not all creeps sleep (Golems, for example, do not sleep), if they are sleeping, you can sneak by them or not fight them. When attacked, however, all of the creeps there will awake and fight back immediately.
As creeps tend to protect items or buildings, being able to sneak by them is a bonus and can get you access to items or useful resources you otherwise would not be able to use.
Your own units will not attack sleeping units without provocation or orders, and upon sunrise all sleeping units immediately awake.
 Advantages to Sleeping
Being able to reduce the amount of enemies fighting you when using Dreadlords, especially a powerful Hero in the higher levels, can help you defeat those of lower levels which are protecting in or do damage to the heroes themselves before they can do significant damage to your heroes.
Also, sleeping creeps do not have to be fought, and if they are protecting such things as Goblin Buildings, or Mercenary Camps, or even items, it's easier to bypass a fight and go directly to those buildings, as your units will not fight them, nor will they fight back until morning has come.
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