Jerrod:
It's an automatic control center for small appliances like coffeemakers and electric skillets.
What you did was to unreel the appropriate cord for your appliance, connect it, and then set the clock/timer for the time you wanted the appliance to come on. This was considered very luxurious and convenient in the '50s.
There were variations of these from several manufacturers. This one is slightly unusual in that it has cords built into it, on reels to keep them wound up and neat. Most "appliance centers" just gave you a number of outlets to plug things into, using the detachable cords provided with the appliances.
Appliance centers surface occasionally, but they are not very common. They were expensive, and many ranges of the era offered a timed "convenience outlet" on the backguard, which was sufficient for most peoples' needs, which usually consisted of starting the electric percolator in the morning.