Reye's syndrome is a very rare complication of the use of aspirin or other salicylates (such as ibuprofen) to treat the symptoms of influenza in children. It is potentially fatal, is often fatal even with treatment, and often causes severe neurological impairment even in patients who recover.
The exact mechanism of Reye's remains a mystery. It was only after years of epidemiological research on patients with similar symptoms who died after suffering influenza that the link to aspirin became clear. How aspirin interacts with influenza to cause a potentially fatal disorder is still unknown, as is the reason why the syndrome only affects children and not adults and why not all children who are given aspirin develop the syndrome.
Aspirin is generally a safe drug when used in moderation. However, packaging for aspirin and other salicylates now carry a warning not to give the drug to children if influenza is suspected, and manufacturers also suggest children not be given aspirin even if only a cold is suspected. Influenza is rarely fatal in children (less than 1%) and the risk of Reye's in a patient who is given aspirin is actually much higher. When flu is even suspected, Acetaminophen is the drug of choice.
In Finding Judas, House suspects the five year old patient has Reye's after he learns she spent time with a teenage babysitter.