Extenuating circumstances are life factors that make a crime seem slightly more understandable. Until recently, she was a pillar of the community, paying her taxes in full and on time. Then her child was diagnosed with cancer, and her insurance wouldn't cover all his medical costs. The woman defrauded the IRS because she needed money to pay for chemotherapy. Courts would consider this an extenuating circumstance.
Aggravating factors are bits of information that make the crime seem more reprehensible than normal.
Burglary is clearly wrong, but burglarizing a series of homes is worse. In addition, all the homes belonged to minority families. In very general terms, the more mitigating factors and extenuating circumstances the court system finds, the lighter the punishment. The more aggravating factors, the more lengthy the sentence. The report may or may not give an explicit sentencing recommendation, but the officials' opinion is usually implied.