If you call someone neurotic, you are saying she is stressed out. Neurotic can be a psychological term or it can be used more loosely. You may have a neurotic tendency to bite your nails or to pull out your hair. Ouch.
The adjective neurotic refers to someone who shows signs of mental disturbance but does not indicate complete psychosis. Neurotic comes from neuro-, from a Greek word for "nerve." It can also describe someone with neurotic behaviors, so you can think of a neurotic as someone who has a particularly bad case of nerves.