GDPR Article 4 Definitions, Article 28 Processor
Controller means the natural or legal person, public authority, agency or other body which, alone or jointly with others, determines the purposes and means of the processing of personal data.
Processor means a natural or legal person, public authority, agency or other body which processes personal data on behalf of the controller.
The clear identification of the controller and the processor is an important step in defining the rights and obligations set out in a contract for the processing of contract data.
A company rents servers in a data center. The company is "controller", the operator of the data center is the "processor". The controller decides on the means and purposes of data processing, i.e. he decides how many servers are provided, which programs are installed there, which data is processed. The processor only acts on the instructions of the controller.