Breakfast jumpstarts your metabolism and so helps you burn more calories throughout the day.
When you eat breakfast you're telling your body that there are plenty of calories to be had for the day. When you skip breakfast the message your body gets is that it needs to conserve rather than burn any incoming calories.
When you eat clean and healthy, your body is getting what it wants and needs. When eating processed (junk) food, your body needs to hold on to what it has because you are depriving your body of what it needs to survive.
So if you want to lose weight, you need to eat. Just make sure your food is your medicine, not your poison!