Writing a research proposal
If your supervisor asks you to formalise your idea as a research proposal (this is not always a requirement) this needs to define a clear research question.
You should also be prepared to explain how this contributes to and develops (or challenges) any existing theories in the field.
It’s important to tailor your proposal to the department you’re applying to.
Different departments may also have different format requirements (e.g. word limit, content) so it’s important to discuss these with your potential supervisor in advance.
For more general advice on how to write a good proposal, see FindaPhd.com.