Sleeping increases your Blockhead's energy which makes your Blockhead move and work much faster. There are three different types of beds that can be crafted; a wooden bed, soft bed, and golden bed. Each increasing the rate of which your blockhead energy is regenerated,

Female Blockhead sleeping in dyed soft bed.


Sleeping in a bed also gives you a gamecenter achievement.

When every player on a server sleeps, (or meditates), the time goes 20 times faster than normal.