A syndrome is a collection of recognizable traits or abnormalities that tend to occur together and are associated with a specific disease.
A syndrome is really a collection of traits or distinctive features that run together. In fact, that's the origin for the term, is from the Greek "syn", for "together", and "drome", for "run". So this is a collection of findings that you tend to see in a number of individuals who otherwise aren't related. Most syndromes are named after the physician who first noticed them in people. So that, for instance, Down syndrome is a condition that was first noticed by a Dr. Down. Marfan syndrome is a condition that was first noticed by a Dr. Marfan. There are a whole list of these, or really hundreds and hundreds of syndromes have been described mostly over the last 150 years or so in medicine, and often named after the individual who first noted that these traits tended to run together.