Neuroticism is a term that refers to a major personality trait in psychology. Neuroticism is a negative personality trait that is on a continuum whose poles are neuroticism and emotional stability.
People who are neurotic tend to experience very negative emotions. These are people who are likely to feel anxious, to get angry, or to be stressed. They can suffer from such things as hypochondria and depression. These are people on whom negative stimuli have a large effect. They are not good at coping with whatever life throws at them.
Since neuroticism is part of a continuum, different people will have different levels of neuroticism. It is not as if a person is either neurotic or stable. Instead, people's personalities are arrayed on a continuum with varying levels of neuroticism.