If you are schizophrenic, you suffer from a mental disorder that includes auditory hallucinations and paranoid behavior.
Schizophrenics used to be thought to have "split personalities," and the roots of the word attests to that early understanding. The word schizophrenia combines the Greek skhizein, "split," and phren, "mind." Now, the disease is understood differently, but schizophrenic is still sometimes used to refer to anything that changes erratically. A movie that's alternately enthralling and boring might be said to be schizophrenic in its pacing.