A squillion is a joke number. It is not a real amount, like a million or a billion — nobody could tell you how many a squillion is, because there is no answer. People invent it to mean "a huge amount, more than I can count, and I am exaggerating on purpose." It is most often used about money: "he must earn a squillion dollars a year." It works like a normal number word in a sentence — you can say a squillion, squillions of, and even squillionaire for a very rich person. The tone is light and playful, and it is more common in British and Australian English than American. Because it is obviously not serious, it also lets a speaker complain or boast without sounding like they are lying — everybody understands the number is made up. Never use it when a real figure is expected.