When anyone refers to cloud computing, they assume that it means that it is something that runs on a system on the internet. While that is not wrong, it is much broader than that. It is not restricted to the type of hardware or the location that it runs, but also in its delivery. Cloud computing is the use of technology to deliver information technology services to reduce costs and better utilize resources. There are three forms of cloud computing in general use today:
Software-as-a-service is a way delivering software as a rental. It is provided through a browser or a local application that is metered using a connection to a server online. The easiest example is that of Adobe which now sells its famous suite of products using monthly software rentals on its Creative Cloud.
The platform-as-a-service concept is unlikely to matter to end-users much but allows them to access services sold on top of another platform. Take Salesforce as an example. It is a CRM SaaS that also functions as a PaaS, allowing other vendors to create applications that take advantage of and run on top of their platform.
This is where infrastructure (servers, databases, networks etc) is provided as a service. Most cloud computing providers have IaaS options. When an administrator looks to migrate the on-premise data center to the cloud, most of the resources in use will be IaaS components like servers. While IaaS can be used to run the above workloads, it is far more efficient to utilize tools created for that purpose.