Most people don't realize that 90% of our sensory input is visual in nature. The remaining 10% is shared by the senses of hearing, smell, taste and touch. Also, 40% of the mass of the human brain is dedicated to vision. One benefit of closing our eyes is that there's a mild reduction of blood, nutrients and neurological activity going to the brain's visual center - and uptake of these qualities in the remaining four senses of hearing, smell, taste, and touch. Therefore, the other four senses, along with the emotional and cognitive portions of the brain gain some temporary sensitivity.
When we close our eyes, it causes an increase in our ability to feel affection. So, if we are singing about something we love: whether that is our country, our significant other, a pet, etc. it causes our affection and emotions for that person to become intensified. A similar phenomenon occurs when we taste a delicious dessert or smell a favorite flower, etc. It is not just our Even a person with excellent vision will instantaneously increase their sense of touch a - by just closing their eyes.
Singing is not only a very multi-sensory experience - it's an intensely emotional experience. Closing one's eyes while singing leads to increased auditory acuity and improved vocal control - which acts as a type of biofeedback. This allows the singer to express an enormous amount of energy at the moment as it becomes a larger-than-life experience. This burst of emotion acts an as a contagion and pulls us into the singer's emotions, and many of us will feel that excitement along with the singer.