A simple explanation from the Spiritualists' National Union:
"What is Mediumship?
The main aim of mediumship is to provide evidence of survival of the human personality beyond physical death. Mediumship is a transfer of information from the spirit of a deceased person via a 'medium' to a 'recipient'.
A medium has the ability to receive information from a communicating spirit and pass on that information. In many respects this will be personal to the recipient of the communication."
The last paragraph is important in helping differentiate psychic sensitivity/awareness from mediumship, issues commonly misunderstood.
Where the beneficiary of information is the individual herself/himself then it's psychic sensitivity.
When communicated information is for the benefit of a third person it's mediumship.