A psych consult is a request from a non-psychiatrist attending physician, usually an internist, but occasionally a surgeon to have a psychiatrist (often a resident) provide a written report on the mental state of a patient for the attending's use. An attending will often request such a consult when they suspect the patient suffers from some type of mental illness that is masquerading as a symptom of a physical illness, or when the patient's mental state may affect their treatment.
Gregory House rarely consults other specialists (except to send them on wild goose chases), but he does frequently seek out psychiatric consultations for his patients as neither he nor none of his fellows have the skills it usually takes 5-7 years of training as a resident to develop.
The psych consult should not be mistaken for a psych referral. If House determines that a patient only has a mental illness, he will generally resign as the attending and let a psychiatrist take over. With a consult, House remains in control of the case and takes responsibility for the result.