Renter credit check is a report that is ran on a new applicant. This report usually contains credit information and prior rental history. It should scan local eviction databases to ensure that your new renter hasn't had problems before. Most landlord will not rent to a applicant if they have been evicted before, often referred as a unlawful detainer.
The tenant credit report should be run on all applicants over the age of 18 regardless if they are going to be contributing financially. If you ever have to evict the people occupying your rental unit, you want as much information as possible on each adult living in this unit. The more thorough of a renter credit check you perform, the more prepared you will be if something goes wrong.