A syndrome is a disease which has established diagnostic criteria but has no clear underlying etiology. In other words, the disease can be diagnosed, but the mechanism of how the disease works is unknown, even though the cause may be known. Syndromes are generally named after the physician or scientist who first describes the diagnostic criteria.
Syndromes are occasionally renamed when the underlying etiology is understood. As such, Downs' Syndrome (called Mongolian Idiocy by Downs himself) was renamed Trisomy-21 when it was understood the syndrome only manifested itself in individuals with three #21 chromosomes. Similarly, AIDS was first known as gay-related immune deficiency until non-gay patients appeared with the disease. Hoewver, the "S" in AIDS still stands for syndrome even though the etiology of the disease is now very well understood.
Another commonly known syndrome is Reye's syndrome. Although the cause is known (giving aspirin to children with flu), it is still unknown why aspirin results in the symptoms of the disease or why it affects some individuals and not others.