A zillion is a huge but nonspecific number. If your favorite café is so crowded that there's barely room to stand, let alone find a place to sit, you might say there are a zillion people in there.
Use zillion when there are so many things or people that it would be hard to count them all. Zillion sounds like an actual number because of its similarity to billion, million, and trillion, and it is modeled on these real numerical values. However, like its cousin jillion, zillion is an informal way to talk about a number that's enormous but indefinite. Experts believe it started as 1920s African-American English slang.