1) Your larynx needs water to operate effectively
The outer layer of the vocal folds is watery mucosa, which protects the vocal folds from vibratory stress. When you consider that the average speed of vibration for female speakers is 210hz for women and 120hz for men, the vocal folds are put under enormous amounts of stress, just in one vibratory cycle. Just imagine rubbing the same spot of skin 120-210 times per second, that is what your vocal folds are enduring. The watery mucosa is therefore essential in the protection of the vocal fold tissue.
So, what happens when you are dehydrated? Well, when the larynx isn’t efficiently hydrated, the mucosa thickens. With a thick sticky mucus on the vocal folds and other tissue within the larynx, you a) end up with flehm which doesn’t sound too pretty and b) you reduce the protection which the mucosa provides. This means the vocal folds are more sensitive to the vibratory stress, which puts the singer at risk of vocal pathologies. Nodules is an example of a vocal pathology which is caused by vibrationary stress.
As well as this, when the vocal folds are efficiently hydrated, they are far more pliable. This means you will feel like singing is easier and can cover more range. It also means your vocal flexibility will improve.
2) It takes a long time (if ever) for the water you drink to reach the larynx
When you drink water, it literally takes hours to reach the vocal folds, if at all. What usually gets forgotten when singers think about drinking water, is that all of your vital organs will take what they need first (to keep you alive). If you are about to sing and your voice feels dry, drinking a cup of water will not hydrate your vocal folds directly. Although you may feel as if your thirst has been quenched, you need to consider digestion time and how in-need of hydration you already were at the time of consumption. In actual fact if you are feeling thirsty, then you are probably already dehydrated as your body is telling you that you need to drink. Therefore, as a singer it is imperative that you are consistently hydrated and aren’t relying on a last-minute tipple to get you through the show.
3) Some drinks, foods, medications and environmental factors will dehydrate you
Cut the crap, here’s a list!
Salt– Increased salt in the blood, causes a build-up of osmotic pressure, which causes the cells in your body to lose water.
Antihistamines, anti-inflammatory and laxatives –Antihistamines especially, are designed to reduce the mucus caused by allergies, in order to relieve symptoms. However, that means they can dry the necessary mucosa in the larynx.
Caffeine– Although generally thought to dehydrate, coffee (moderate dose: 4mg/ 4 cups per day) has actually been shown in some studies to contribute to daily hydration and doesn’t have a negative effect on fluid balance. However – watch out for the reflux.
Alcohol – Small amounts of alcohol were found to show minimal effects on hydration, however, the stronger and larger the serving size, the more detrimental to hydration status.
Dry, dusty, air-conditioned environments – The larynx and therefore the vocal folds are located just above the trachea (windpipe). This means anything you inhale, will directly impact the vocal folds.
Killer, S; Blannin, A; Jeukendrup, A.  No Evidence of Dehydration with Moderate Daily Coffee Intake: A Counterbalanced Cross-Over Study in a Free-Living Population. Online at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3886980/
Polhuis, K; Winjen, A; Sierksma, A; Calame, W; Tieland, M.  The Diuretic Action of Weak and Strong Alcoholic Beverages in Elderly Men: A Randomized Diet-Controlled Crossover Trial. Online at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5537780/