A more thorough explanation:

The appreciation test is a legal test used in criminal law to determine if a defendant is not guilty by reason of insanity. It requires clear and convincing evidence that at the time of the crime, the defendant suffered from a severe mental disease or defect that prevented them from understanding the wrongfulness of their actions.

For example, if a person with severe schizophrenia commits a crime, they may not understand that their actions were wrong due to their mental illness. In this case, the appreciation test may be used to determine if they are not guilty by reason of insanity.

The insanity defense is an affirmative defense used in criminal law that alleges a mental disorder caused the accused to commit the crime. Unlike other defenses, a successful insanity defense may not result in acquittal but instead in a special verdict ("not guilty by reason of insanity") that usually leads to the defendant's commitment to a mental institution.

For example, if a person with severe bipolar disorder commits a crime during a manic episode, they may not have had the mental capacity to understand the wrongfulness of their actions. In this case, the insanity defense may be used to determine if they are not guilty by reason of insanity.

The black-rage insanity defense is a type of insanity defense based on an African-American's violent eruption of anger induced at least partly by racial tensions.

For example, if an African-American person commits a crime in response to racial discrimination and violence they have experienced, the black-rage insanity defense may be used to determine if they are not guilty by reason of insanity.