This was a slogan first invented by a [well-known cereals company] about a century ago, in a bid to persuade people to include cereal (which was a new thing) as part of their breakfast. In truth, it’s meaningless, because what it’s actually saying (quite truthfully) is “For most of your nutritional needs, you need to eat other things.”
Cereal is mostly carbohydrates (wheat, usually) and sugar—lots and lots of sugar (which is—not fat).
For an idea of what a healthy breakfast really looks like, visit a kibbutz in Israel. There, for breakfast, people eat fresh salad (tomatoes, cucumber, spring onions, olives, which they cut up themselves—the finer, the better—then add salt and extra virgin olive oil), other fresh vegetables, low-fat plain yoghurt, cottage cheese, a couple of slices of fresh bread, orange juice or fresh fruit, and coffee.
As “Deputy Food Manager” (= food stores gofer) at one such kibbutz many years ago, it was my job to ensure that the breakfast buffet was kept stocked with all items. On one occasion, the radishes ran out—but there were none left in the kitchen walk-in refrigerator. So I jumped on a tractor, drove out to the nearest radish field, fetched some more, brought them back, washed them, and restocked them in the buffet. As I pulled them out of the ground, I couldn’t help thinking “Eat your heart out, [well-known cereals company]: it doesn’t get better than this…”
(Originally written in reply to a question at Quora.com)