Well I'm not a scientific expert either but this is what I understand.
Mitochondrial DNA is written as MtDNA and it is found in hairs. It is passed through the maternal side of the family so if a hair was found, scientist could say that it could belong to me or any of my children - but that is all. There were huge studies done on MtDNA and because they were clinical studies, they had a lot of data about the donors of the MtDNA. For this reason, they were able to make a database with this information and that database includes details about race. This means that if they find a hair at a crime scene, they can look up the database and make an educated guess at the race of the hair's owner. In the trial of David Westerfield, some blonde hairs were found in his RV. Experts were able to say that some of these hairs had come from Brenda vanDam or one of her three children. However, another hair, they said was Asian in origin. This was puzzling - because it was blonde and Asians are not blonde. It transpired that David Westerfield had a girlfriend who was Asian but who had died her hair blonde!
Nuclear DNA is found in blood, skincells etc and it is pretty unique to individual people. You will inherit some DNA information from your parents and so scientists can tell if two people are likely to be related. They can also tell sex from nuclear DNA but not race. This is because they would need to define race! The mtDNA database is different because they have such a huge bank of data inlcuding race.