First, as an individual becomes more overweight or obese, one area of the body that becomes larger in circumference is the neck. Therefore, a large neck likely corresponds to increased fat tissue elsewhere in the body. Aside from having a large stomach, there will also be tissue crowding along the airway, especially in the throat. When the airway becomes narrowed, it is more likely to partially collapse (causing hypopneas or snoring) or completely close off (causing sleep apnea). If an individual has enlarged tissue in the back of the mouth and throat -- such as big tonsils, adenoids, or tongue -- this will likewise contribute. The weight of the neck tissue itself may also lead the soft airway to collapse.
The circumference, or distance around the neck, is typically measured with a paper measuring tape at the doctor's office. In general, this is considered to be a risk factor for sleep-disordered breathing when the circumference is greater than 17 inches for men and 16 inches in women.
For the reasons described above, neck size can have a significant impact on your ability to sleep. Sleep physicians will often measure neck circumference since it can be as useful as height and weight to determine your risk of having breathing problems during sleep. In the right context, it may be additional evidence suggesting the need for further evaluation.