This is the key thing. Previous to 'cloud' as a customer, you'd pre-pay for X amount of rack space, plus energy usage, and if not providing your own kit, X amount of hardware. And then there was the separate billing for management (basically hands-on reboots, or kit recabling). Then there was the (often separate) arrangement for secure network access from your offices to the data centres.

Cloud got rid of all of that. These days you sign a contract, and cherry pick what resources you need from a shopping list, and it's all provisioned in the background, and then deprovisioned when you don't need it anymore. Behind the scenes its all the same stuff it used to be, but now it's all wrapped up in a single service.

Companies love cloud because it means they no longer need a large infrastructure team to manage the server stuff which is a saving, along with the more fluid pricing model - also a saving.