Pedophilia (British spelling: "paedophilia") is sexual attraction to children. The psychiatric definition (see Diagnostic and Statistical Manual of Mental Disorders, 4th edition, American Psychiatric Association) states:
Diagnostic criteria for 302.2 Pedophilia A. Over a period of at least 6 months, recurrent, intense sexually arousing fantasies, sexual urges, or behaviors involving sexual activity with a prepubescent child or children (generally age 13 years of younger). B. The fantasies, sexual urges, or behaviors cause clinically significant distress or impairment in social, occupational, or other important areas of functioning. C. The person is at least age 16 years and at least 5 years older than the child or children in Criterion A. Note: Do not include an individual in late adolescence involved in an on going sexual relationship with a 12- or 13-year-old.
Sometimes, however in popular use, the word "pedophilia" is used to describe sexual activity with underage adolescents; while such activity is illegal, it is often only borderline pedophilia or not pedophilia at all, by the medical definition.
Sometimes a clinical distinction is made between pedophiles and "situational offenders" (a distinction though that is not reflected in the above DSM-IV definition). A pedophile is a person whose primary sexual attraction is to children, while a situational offender is someone who engages in sexual activity with children not as their primary sexual preference but due to a particular situation they are faced with, and would not otherwise engage in such activity except for that situation.
Most cases of father-daughter incest, for example, are believed to involve fathers who are situational offenders, rather than pedophiles. The particular situation which gives rise in that case to the sexual abuse is generally the absence or withdrawal (especially due to mental illness) by the mother.