Why is it important to ensure that a patient is well hydrated and that his electrolyte levels are no

Your electrolytes are critical for nearly all body functions - metabolism, nerve conduction, etc. If the electrolytes are abnormal, you can see decreased function in different systems. Also, in order to maintain an appropriate electrolyte balance, you need to remain adequately hydrated. That's why sports drinks like Gatorade are often best for you if you're sweating a lot (losing a lot of electrolytes), although they may not be best if you are losing fluids through vomiting or diarrhea. In those cases you may be losing significant quantities of water, but not necessarily electrolytes.

In the medical setting, we can administer 0.9% NaCl solution to replace lost fluids and sodium, but in a case of dehydration and electrolyte loss, we will opt for a solution call "Lactated Ringers" which in simple terms is Gatorade without the colors and flavors that we run directly into your veins.

Just to add on to his answer severe dehydration can cause shock that's why you have to rehydrate the patient!