Full definition
Data processor is defined as: A data processor is a supplier that handles personal data on behalf of a controller, strictly following the controller's documented instructions.
The processor's role is defined by the controller's instructions. A processor that decides to use personal data for its own purposes stops being a processor for that activity and becomes a controller in its own right, with its own GDPR duties.
Processors must give controllers the information needed to demonstrate compliance, including evidence of technical and organisational security measures and any use of sub-processors.