A crime of passion is a crime that is committed under extremely emotional circumstances. A primary example of this would be a man who comes home to find his wife in bed with another man, and he attempts to kill the man. If a defendant claims that their crime was a crime of passion, then they are asserting that it was not premeditated.
People occasionally commit crimes as a direct emotional response to a very charged situation. This is called a crime of passion. It is sometimes said that a "fit of rage" came over the person. In the instance of murder, if the jury believes that it was a crime of passion, then the death penalty can be avoided, and a lesser sentence can be given. Intent is needed for a murder conviction; so, the jury may only convict the defendant of manslaughter.