A zillion is a huge, made-up number. It is not a real amount you could count — it is the way people say 'so many I cannot count them, and I am not going to try'. Someone invented it about a hundred years ago by copying the sound of million, billion, and trillion, so it feels like a number even though no number is behind it. You use it when you want to complain or be dramatic in a friendly way: 'I've told you a zillion times.' 'There were a zillion mosquitoes.' It works like a number word, so it takes 'a' or a plural: 'a zillion emails', 'zillions of stars'. Very often it appears as 'zillions of' when you don't want to name any amount at all. Because it is playful slang, it belongs in conversation, in chat messages, in a funny story — not in a report where a reader expects real figures. English has several of these joke-numbers — gazillion, bazillion, squillion — and they all mean the same thing, just with more sound effects.