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.
It's too common of a problem these days. A landlord has a vacant property, which means losing money day after day. The temptation is all too easy to give into when it looks like you have a well-dressed applicant who seems to be well spoken, and claims to have a good job. But what do you really know about them? Anyone can pull off a good act for the few hours it takes to impress someone, and try and "smooth talk" their way into a rental and avoid the background checks. And if you check their job references, many people will just use their friends to take the call and convince you that they're on the up and up. Always verify the background of your applicants!