Answer:
Her sister's 13-year-old son has Autism. Palin's son, Trig, has Down's Syndrome.
EDIT: Correct. Her sister, Heather Bruce, has a son with autism. Also, two of her cousins in her extended family, also have children with autism/Asperger's.
When Senator McCain referred to this intimacy with autism in the debate, it is her varied family experience he was referring to.