What happens to copper(II) hydroxide when it's heated? what's inside its decomposition?
Well,this is a kind of dehydration reaction,and you will come across similar such reactions plenty of times as you read about the effect of heating on various compounds.

I am going to approach this in a sligthly different manner: how the copper(II) hydroxide was generated from the copper(II) oxide. 
According to Wikipedia


  Copper(II) oxide belongs to the monoclinic crystal system. The copper atom is coordinated by 4 oxygen atoms in an approximately square planar configuration


So we can think of it this way,that when water was introduced in the copper(II) oxide powder,the water molecules entered into the voids(in a stoichiometric fashion)of the oxide lattice.Mind you,this is just a way of visualization,but it can help a lot. So now,when you are heating the hydroxide in a controlled manner,then we can imagine that the water molecules residing in the voids escape out,leaving the oxide in the same oxidation state. (Also,now you should keep in mind that most hydroxides lose one or more molecules of water to form their respective oxides)

Note: if heating is done excessively,then the oxide itself can decompose to a variety of products