Where do you think it got its name? You're breaking the fast from the night before. Breakfast kick starts the metabolism, giving the body energy, and caloric content enough to carry you till your next meal. An easy way to remember HOW much to eat is this. Eat like a king at breakfast, a prince at noon, and a pauper at night! A well balanced, and portion controlled meal is always best! :)
That saying probably started when we were less industrialized and technologically advanced. So people started with a large breakfast, because they actually worked it off with physical labor before the mid-day meal.
It fuels you up for the rest of the day. Breakfast is the first meal of the day, when you still have the whole day ahead of you. By lunchtime your day is about half over. At dinnertime most of your day is done. The fact that we eat our smallest meal to prepare for the day ahead and our largest meal when it's over is entirely backwards.
I don't think it is, that saying started when almost everyone had physical labor for jobs so you needed a big breakfast but I have a lot of friends that have a small to no breakfast at all (just because they want to sleep in and still get to school one time) and they have all A and B in there classes