A psychiatrist is a physician who specializes in psychiatry - the treatment of mental illness and diseases of the mind. Psychiatrists are medical doctors and differ from psychologists in their ability to prescribe drugs.
Whenever House's differential includes a mental illness, such as post-traumatic stress disorder or Munchausen syndrome, House often wants to refer the case to a psychiatrist as he doesn't want to deal with psychiatric disorders. It appears House has a deep distrust of psychiatrists and is dismissive of their skills. This is clearly seen in the episode Frozen where House treats a psychiatrist over the internet and, despite his obvious attraction to her and her insights into his personality, he is dismissive of her efforts to psychoanalyze him.