Examples of mitigating circumstances...
Victim culpability. The victim willingly participated in the crime or initiated the events leading to it. If Domingo started a fight by attacking Walter and Walter responded with more force than was necessary to defend himself, this factor would come into play at Walts assault-and-battery sentencing.
Difficult personal history. The defendants unique upbringing or family circumstances led to her criminal conduct. For example, a lawyer might try to persuade a sentencing judge that the clients violent acts are attributable to abuse she suffered as a child.
These are just two examples.
Source:
http://www.nolo.com/legal-encyclopedia/mitigating-circumstances-sentencing.html