I liken "cloud" to any service accessible via the internet. This can include the likes of Microsoft's Azure cloud offering, similar "Software/Platform as a Service" offerings from other vendors, dedicated server hosting or shared server hosting solutions which are available much cheaper.
There was some confusion for Windows Phone 7 developers when Microsoft's cloud offering was pitched to students when the "All In" campaign began, around the same time the Windows Phone 7 campaign was getting going.
For developer's the confusion was borne out of wondering how do I support the costs of Microsoft's or other Platform as a Service offerings when my app is going to be free or returning revenues of an as yet unknown quantity.
In a much needed positioning comment offered to windows phone 7 developers, Microsoft made their position clear on Cloud with respect to shared hosting services, their cloud offering and Windows Phone 7 apps.
In short it's a budgeting call. If you're service has the income to cover cloud services (could be from any provider), then it is the most scalable model. Until then, traditional hosting services are recommended.
This is explained in more detail in this post.
Azure Storage and WP7