Electrolysis of copper sulfate decomposes it into its ions, by means of electrical energy. The copper sulfate electolyte solution consists of rich concentration of Cu^(2+) ions and sulfate ions, SO_4^(2-), that can transport the electrical current during electrolysis.
During the electrolysis process, the negative sulfate ions, SO_4^(2-), are attracted to the positive anode, while the positive ions Cu^(2+) are attracted to the negative cathode, that becomes covered with copper deposits.
Electrolysis process can be used in copper electroplating, where the object that needs to be electroplated is the cathode, that have to be a metal and immersed in electolyte solution. Anode object ussualy provides the material that is used in coating. Anode object has to be oxidized to release metal ions that drift accross cathode object.
Hence, any conducting metal can be eletroplated for different purposes, such as decorative (silver electroplating) or protective (chromium plating).