Proper hydration is absolutely an important part of weight loss! Thirst is what we call a late sign of dehydration, meaning you feel thirsty after all your body's other measures to signal you that something is wrong have failed. You don't feel thirsty until you are quite dry!
Most of the early signs of dehydration are easily confused for hunger: fatigue, irritability, distractability, weakness. When most people feel that way, they reach for a snack instead of a glass.
Water is an important ingredient for the millions of chemical reactions taking place in your body and any given time, so if there isn't enough water to be had, your body tries to limit the number of chemical reactions going on. In other words, slowing your metabolism. So people who don't drink enough can actually gain or have trouble losing weight even if they think they are eating and exercising correctly!