This is the American Psychiatric Association's definition of a personality disorder:
"An enduring pattern of inner experience and behavior that deviates markedly from the expectations of the culture of the individual who exhibits it."
In easier terms, it means that a person has a personality characterized by certain traits and behaviors that are abnormal, chronic (not just a 'mood swing', but a life-long characteristic of their personality), and disruptive in their lives. These traits tend to be extremely rigid because the person doesn't view them as wrong, they view them as a 'normal' aspect of who they are. That is why they fall onto Axis II and not Axis I - they aren't a clinical disorder, the patient doesn't view their behavior as disordered or problematic.
Personality disorders are grouped in the DSM based on their characteristics, and there are 10 of them total. They are grouped as such:
Cluster A - Odd/eccentric personality disorders
- Paranoid
- Schizoid
- Schizotypal
Cluster B - Dramatic, over-emotional, erratic disorders
- Antisocial
- Borderline
- Narcissistic
- Histrionic
Cluster C - Anxious/fearful disorders
- Avoidant
- Dependent
- Obsessive-compulsive (this is not the same as OCD, obsessive-compulsive disorder).
There is also a diagnosis of "Personality disorder, not otherwise specified" for people whose behavior is obviously out of the ordinary and erratic, and is clearly a personality feature and not a clinical disorder, but they don't fit into any of the above personality disorder categories.
Hope that helps!