The levels of potassium, sodium, magnesium, etc. get too low which can be dangerous, especially in the case of potassium if you drink too much water..
Some people have more or less need for different amounts of water so I'm not sure what is the best for you. If you exercise or sweat you will need more. 8-10 glasses of 8 ounces each is just a guideline and some question if it's right.
A lot of people don't drink enough water so that's partly the reason it's given attention, and partly because some can use the water cure to help with a specific disease or problem.
The suggestion for the water cure is to put salt in the water if you're drinking a lot of water. A good quality sea salt, not ordinary table salt, will supply sodium and several minerals. If you eat a lot of processed food that's high in salt you may not need salt, but then you shouldn't be eating a lot of processed food.