What is a "Mental Health Background"?

In all of the debate about gun control and background checks this phrase is tossed around as though it means something specific.  What is a mental health background?  What about this "background" can be discovered through searchable records that might be available to sellers of guns?  What research or data are available that correlate episodes of treatment for mental illness with tendency to kill people?  For years people have lied about times in their lives in which they have sought treatment for mental illness because for years such information was believed to disqualify an individual from a job, public service, professional licensing and the like.  This stigma has added not only to the burden they carry from their illness, but also their reluctance to seek help. Only in the last decade have we begun to acknowledge that those experiencing mental illness can live productive lives in society if they receive the treatment they need.  Treatments are increasingly available on the same terms as treatment for other illness.  Do those advocating a  check for a "mental health background" believe they have a right to inspect the records of such treatment?  Medical records are not considered records in the public domain.  We believe in the right to privacy with respect to such personal data.  How is all this expected to come together in a background check that can be performed from a gun store in any place in the country?  Who might be helped by such a requirement?  Who might be hurt?