Responsible Person is an individual who is responsible for making payments of specific nature on behalf of payer/deductor.
For example:
Company: CFO or MD/ Director of a company who is making payments on behalf of company is a responsible person.
LLP: Managing Partner of LLP who is making payment on behalf of LLP is a responsible person.
Individual: The Individual himself is a payer and responsible person for making payments and deducting TDS.