Dedicated power means, its a line all its own, like for a fridge so nothing causes an overload and trip the ciruit.
lets say the fridge draws 15 amps and a microwave draws 15 amps ( 30 amps combined)
Now you are away from home and the fan is running, then the fridge kicks on, drawing 30 amps on a 15 or 20 amp outlet.... now you come home to spoiled food since the circuit tripped.
Microwaves do the same thing with the high draw.... so nothing else can be on those lines.