As the proprietor of an ever-growing tower, you'll choose which businesses to add to your skyscraper (depending on the desires of the "bitizens" that inhabit it). Then it's your job to watch over the businesses, keeping the shelves stocked and the stores staffed. As products are sold over time, you'll earn coins that can be applied to a new floor of your building and the terrifying cycle continues.
The secret to Tiny Tower is in the passage of time. Products take time to restock and sell out, and time continues to progress even when you're not playing. As a result, there's always a reason to check in on your tower, whether it's to use the game's elevator to bring a new bitizen to your apartment housing, or just make some more nachos for the bar.
If you get really impatient, you can spend in-game currency called Bux to speed things along. You'll earn these for menial tasks like helping to find a specific tower resident, but they can also be purchased for real-life money. Of course, the game itself is free, so if you're patient enough, you can enjoy everything Tiny Tower has to offer without spending a cent. You are patient enough, aren't you?
Spoiler: You are not.