So let's begin with some definitions for the word syndrome.
From http://www.merriam-webster.com/dictionary/syndrome
Definition of SYNDROME
1. : a group of signs and symptoms that occur together and characterize a particular abnormality or condition
2. : a set of concurrent things (as emotions or actions) that usually form an identifiable pattern
Also, from http://medical-dictionary.thefreedictionary.com/syndrome
Syndrome /syn·drome/ (sin´drōm) a set of symptoms occurring together; the sum of signs of any morbid state; a symptom complex.
Now, let's move on to definitions for thoracic outlet.
From http://www.thefreedictionary.com/Thoracic+outlet
The cavity that exists between your first rib and your clavicle is filled with nerves, veins, and muscle When any of them become compressed, a condition called thoracic outlet syndrome (TOS) can develop The cavity that exists between your first rib and your clavicle is filled with nerves, veins, and muscle. A Quick Look at Thoracic Outlet Syndrome by Big Oak, Inc.
More on just what the thoracic outlet is can be found here - http://ergonomics.about.com/od/Thoracic_Outlet_Syndrome/f/what_is_thoracic_outlet_syndrome.htm
So now we put it all together.
From http://medical-dictionary.thefreedictionary.com/syndrome
Thoracic Outlet Syndrome- any of several neurovascular syndromes due to compression of the brachial plexus nerve trunks, with pain, paresthesias, vasomotor symptoms, and weakness and small muscle wasting in upper limbs; causes include drooping shoulder girdle, a cervical rib or fibrous band, an abnormal first rib, limb hyperabduction (as during sleep), or compression of the edge of the scalenus anterior muscle.