According to Legal Dictionary ~ Law.com
noun. in criminal cases, particularly homicides, actions of the accused or the situation under which the crime was committed for which state statutes allow or require imposition of a more severe punishment.
"Special circumstances" in murder cases may well result in the imposition of the death penalty for murder (in states with capital punishment) or life sentence without possibility of parole. Such circumstances may include: rape, kidnapping or maiming prior to the killing, multiple deaths, killing a police officer or prison guard, or actions showing wanton disregard for life, such as throwing a bomb into a restaurant.
What are special circumstances in California?
Penal Code 190.2 PC is the California statute that explains the situations where a person can be liable for murder with special circumstances. These are aggravated forms of murder where the defendant, if convicted, can be sentenced to life in prison without the possibility of parole, or the death penalty.