Thanks to all of you!

"Bazillion" is one of a number of nonstandard words that mean an indefinitely large number. See the Wikipedia article, https://en.wikipedia.org/wiki/Indefinite_and_fictitious_numbers#-illion Sometimes people make them up. Some have become common enough that you could call them informal words. Right now, I can't guess, without checking, whether or not I will find "bazillion" the dictionary. I just checked: ahdictionary.org does not include "bazillion," but it does include "jillion." The real words ending in -illion are troublesome, because, except for "million," there is--amazingly--ambiguity about what they mean--and in various countries the meanings have changed with time! When I was growing up, a "billion" meant 1,000,000,000 in the United States; that is, a thousand million; but it meant 1,000,000,000,000 in the U.K; that is, a million million. But nowadays, "a billion" means 1,000,000,000 in the U.K.! All I can say is, be careful when reading and be sure you understand which meaning is meant. When writing, either avoid using "billion" and "trillion," or be sure to give a clue to let people know what you mean!

"Bazillion" just means "a lot." It's not an actual number of things. There's also "zillion" or "gazillion" that mean the same thing. Not commonly used by adults (at least, in my experience), mostly by kids.