The following is the most comprehensive and accurate definition of empty nose syndrome (ENS) available today.  The below definition was copied from the wikipedia article on ENS with only slight modifications.  

Empty nose syndrome (ENS) is a medical condition that is caused when too much inner nasal mucus-producing tissue (the turbinates) are cut out of the nose,  leaving the nasal cavities too empty, too wide and too dry, with severely diminished capabilities to perform their functions of conducting, filtering and humidifying the inhaled air to the lungs and with severely impaired capabilities to preserve themselves and regenerate.  Before reading further, please note that the symptoms of ENS can range from mild and annoying to severe and highly debilitating. While common elements generally exist among sufferers, the level of suffering can vary considerably.   

These operations, known as 'turbinate resections', 'turbinectomies', or nasal 'conchotomies', are performed by ear, nose and throat specialists or by plastic surgeons for different reasons. The most common reason to operate is chronic hypertrophy (enlargement) of the turbinates, which can block too much of the air passage in nasal airways. Among the most common causes for this condition are allergies, hormonal imbalance, too much exposure to dust, smoke and other airborne irritants, nasal structural deformities like a deviated septum and prolonged use of intranasal decongestants.

Right inferior turbinate with its front cut off, showing the unique turbinated structure of the turbinate

What are terms used relating to empty nose syndrome, and what are some important functions of the nose?

The term empty nose syndrome was originally coined in the 1990's by Dr. Eugene Kern who was at the time head of the Otolaryngology ward of the Mayo Clinic in Rochester, Minnesota. He and his colleagues began to notice that more and more patients who underwent turbinectomies seemed to develop symptoms of nasal obstruction and shortness of breath even though their noses appeared to be wide open. Other symptoms were nasal dryness, dryness in mouth and throat, eye dryness, shallow unrestful sleep, diminished sense of smell, difficulty concentrating, and quite often clinical depression. All the patients' CT scans showed that they had very wide and almost totally empty nasal cavities, thus they called it the empty nose syndrome. Dr. Kern then went on to give a series of lectures on ENS, and later summarized his findings in a medical article.

The nose has many functions, besides it being the most prominent feature that shapes our face: breathing, smelling, humidifying, heat regulating and filtering the inspired air to meet the requirements of the lungs for optimal rate of function and gas-exchange, supplying the lungs with just the right amount of respiratory resistance. In fact, the nose provides more than 50% of overall airflow resistance to the lungs.  When the turbinates are largely removed, the nose is unable to provide these critical functions.

Front cross CT sections of nasal cavities - Before and after a total inferior turbinectomy. Note how this patient's nasal mucosa is trying to compensate by thickening of the mucosa on the septum and the right middle turbinate. This patient now suffers from ENS

When too much of the turbinates are resected, the nose loses its capacities to properly pressurize, direct, temperature regulate, humidify, filter, smell and sense the inspired airflow. The natural synchronization of breathing between the nose, the mouth and the lungs is also impaired, and the result is an empty, dry and crippled nose, which feels too empty and at the same time non-functional. People suffering from empty nose syndrome feel a constant inability to take a deep, satisfying breath through their noses, their sleep becomes very shallow, and many also develop sleep apnea. ENS sufferers tend to be depressed and anxious, which may cause them to avoid social interactions. Some experience problems such as Sinus pressure, nasal or facial pain.

What is Paradoxical Obstruction?

ENS is physically characterized by grossly and abnormally enlarged airways because of the loss of the inferior or middle turbinates. This has a dramatic impact on the quality and features of the inhaled air through the nose, which results in significant breathing difficulty known as "paradoxical obstruction." This obstruction is caused by a multiple of pathological factors that occur when the turbinates are removed:

a) The airflow becomes too turbulent, hence less air gets conducted efficiently through the nose to the lungs.

b) The trigeminal airflow motion and temperature sensing receptors, embedded in the nasal mucosal layers, do not get stimulated enough, and this registers in the brain's breathing centers as a breathing obstruction.

c) The dramatic loss of humidifying, filtering and heat-transfer tissues of the turbinates reduce the quality of the air that does reach the lungs, and this results in less efficient gas exchange at the alveoli of the lungs.

d) Nasal resistance to the lungs drops below the optimal level and this weakens the elasticity of the lungs thus decreasing lung expansion resulting in a less efficient gas exchange.

e) The nasopulmonary neuro-vacular reflex is disrupted. This reflex connects the sensation of airflow in the nose to all activities of the lungs - lung excitation, pulmonary blood flow, rate of expansion, rate of contraction, which all eventually affect the efficacy of the gas exchange process.

f) The altered aerodynamics of the airflow, causes the flow to converge too much into the lower empty cavities of the airway, which in turn prevents proper ventilation of the upper cavities resulting in diminished sense of smell. This further diminishes the sense of airflow motion through the nose, because of synergistic, interactive influences between the olfactory nervous pathways and the trigeminal ones.

g) The constant state of dryness and sub-atrophy of the nasal mucosa induces rhinitis sicca which is a state of reduced blood supply to the mucosa, reduced ciliary activity and mucus secretion, resulting in more dryness and poor waste disposal which accumulates in the nasal passages and throat, which continues to impair and deteriorate all nasal functions, not to mention sensation and reflexes such as the nasopulmonary relefex (mentioned earlier), sneeze reflex, etc'.

The main danger with prolonged empty nose syndrome is developing atrophic rhinitis, which is an inflammatory, degenerating disease of the nasal cavities and sinuses, characterized by degeneration of nasal bone and soft tissue, enlarged nasal cavities and totally dysfunctional remaining nasal mucosa, which is often accompanied by foul smelling secretions (known as “ozaena”), nosebleeds and crusts.

For many years, people with ENS have been automatically labeled as suffering from secondary atrophic rhinitis. "Secondary" implies that the chronic state of nasal atrophy was caused by surgery, as opposed to "primary" in which the atrophy occurs from other reasons that are not induced by medical intervention. ENS is an iatrogenic condition (caused by medical treatment), but does not begin as full blown atrophic rhinitis, although very similar in some of its symptoms (primarily the breathing difficulties and the over enlarged nasal cavities). Nevertheless even in early stages of ENS there is some degree of nasal dryness present, perhaps more similar to sub-atrophic tissues or to rhinitis sicca (a chronically dry nose) than to atrophic rhinitis. Still, it should remain a bleak warning that ENS can develop into full blown atrophic rhinitis.

The main features in ENS are the paradoxical breathing difficulties, sensation of nasal emptiness, and the sensation of an unduly patent current of too cold and too dry air impeding the remaining nasal structures and nasopharynx. To the naked eye, the remaining mucosal tissues usually seem reasonably normal and not grossly atrophic (besides the fact that a large portion of the nasal mucosa's has been lost in the turbinectomy). Over the years, due to ill health or simply initial loss of too much nasal mucosa and blood supply, the remaining mucosa can become drier and drier, and there is a danger that it will go through metaplasia and become grossly atrophic. But this seems to be more of a rarity in western societies today. The reasons for that might be the abundancy of protein, fresh fruit and vegetables, clean drinking water and improved conditions of hygiene. The mechanism of how exactly atrophic rhinitis begins when it still unknown.

Physical symptoms associated with ENS: 

• Paradoxical Obstruction: dyspnea: shortness of breath: a feeling that although enough (and even too much air is entering the nose) but nevertheless one still feels short of air.
• Hyperventilation at the slightest appearance of pressure (physical or mental).
• Feeling of lack of resistance to the lungs when inhaling or exhaling through the nose: difficulty inflating the lungs properly when breathing through the nose.
• Difficulty breathing through nose calmly and slowly.
• Nasal airflow feels too dry and cold.
• Nasal membranes feel dry.
• Either too little mucus production, or conversely, constant unstoppable rhinorhea.
• Nasal pain.
• Annoying feeling of nasal emptiness. Whole sections of the nose, in particularly in the front, feel missing because they are amputated.
• Lack of nasal airflow sensation.
• Feeling that the nose is not ventilated enough.
• Diminished sense of smell and/or taste together with heightened pulmonary sensitivity to highly volatile compounds such as synthetic paint, perfume, cleaning detergents, gasoline.
• Speech problems.  Patients report a sensation of too much air escaping their noses or as if their noses were numb and they can't sense the air as it travels through when speech is performed. Therefore, they sense difficulty in controlling speech and punctuating some words, especially which involve words that are made of soft sounds. Sometimes the voice sounds as if the nose is obstructed.
• Thick postnasal drip or dry, sticky, viscous phlegm build-up in pharynx and throat.
• Heightened pulmonary sensitivity to cold and dry air, to airborne irritants and odors (such as smoke, dust, gasoline and paint fumes, etc'). It is not uncommon for ENS sufferers to develop asthma and chronic bronchitis. 
• Dryness in the larynx, back of the mouth, palette, tongue.
• Dry eyes.
• Sinus pressures and pain (even without clinical symptoms of sinusitis)
• Chronic sinusitis 
• Headaches
• Elevated or unstable blood pressure.
• Crusts in nasal airway.
• Occasional bleeding.
• Foul smell in or from nose.
• Lathergic behaviour or flat affect caused by a lack of oxygen and/or sinus and superior nasal regions pressure.

Sleep problems might also be present: 

• Poor quality of sleep - does not feel well-rested in the morning.
• Nightmares or night terrors.
• Sleep-disordered breathing (SDB) and sometimes full apnea.

Psychological symptoms:

• Depression.
• Anxieties.
• Social phobia (avoidance of social interaction)
• Loss of self esteem.
• Panic in the slightest presence of stress.
• High irratibility.
• Acute stress disorders.

Cognitive symptom:

• Difficulty concentrating (known as "aprosexia-nasalis").