> The cloud is renting someone else's computer at a way higher price than it would cost you to use your own.

This is a simplistic view that doesn't discuss any of the trade-offs inherent in the choice between running your own hardware and using a cloud service.

Yes, it's a higher price, but it allows you to stop paying for it when you stop needing it. You can scale up rapidly. You don't have to deal with buying, maintaining, or replacing hardware.