" Shake off this downy sleep, death counterfeit, and look on death itself.(ll,ii)" - Macduff is telling everyone to wake up. Macduff doesn't see death when it comes to sleep
The word sleep relates to the story because a lot of things happen around the time people are suppose to go to sleep. Macbeth killed Duncan and his guards when they were sleeping. He made there sleep turn into an eternal sleep. Also Macbeth and lady Macbeth are finding it hard to sleep because of what they caused.
a condition of body and mind such as that which typically recurs for several hours every night, in which the nervous system is relatively inactive, the eyes closed, the postural muscles relaxed, and consciousness practically suspended.
" The sleeping and the dead are but as pictures.(ll,ii)" - Lady Macbeth is trying to convice Macbeth that there's no difference betweeen sleep and death. When the guards and Duncan were sleeping, Macbeth killed them.
DEAD Duncan is dead and is having an eternal sleep
END Macbeth put an end to Duncan while he was sleeping