Eating less calories (and those can be calories from fat, carbs, or protein), and burning more calories than you're consuming each day is ultimately what allows you to lose weight. But that being said, there is some evidence that cutting calories from carbs (rather than from fats or proteins) can be helpful in allowing you to lose that weight and keep it off long term.
Here's why: calorie for calorie, fat and carbs make you feel more full than eating carbs do. That means you can cut the same number of calories, but be more satisfied if you're eating a diet that has less carbs in it.
High carb foods that we tend to over consume are also processed foods high in refined flours and sugars. These foods provide little nutritional benefit beyond calories, and are engineered to make our taste buds go crazy. If you're watching your carbohydrate intake, and as a result eat less pasta, cakes, and cookies, it will make losing weight a lot easier.
I don't say there are "good" and "bad" carbs, but there are some carbs that are going to do more for you than others. Carbs that come from fruits, vegetables, whole grains, and beans are going to also come with important vitamins and minerals that help your body run at their best. Carbs from refined sugars and flours, on the other hand, are only providing calories, and not the essential nutrients that whole foods can give you.
As always, how many carbs you should cut differs for different people. So work with a coach to make sure you're cutting carbs safely and sanely, so you can make your weight loss stick!