If we talk about "Cloud Computing", it's mainly about three different kind of services: "Infrastructure as a Service" (IaaS), "Platform as a Service" (PaaS) or "Software as a Service" (SaaS). Let's take a look at each.
Let's take a start-up company that wants to offer a cloud-based service: the young company could set up a web server, set up network services and more. It is more likely nowaways, however, that the start-up books the virtual server "EC2" (Amazon Elastic Compute Cloud) from AWS (Amazon Web Services), which provides the required services: Server power, computing capacity, storage capacity and network services. And the best thing about it is: The start-up always pays only as much as it actually uses ("usage-based charge models") and at the same time the required computing or storage capacity can be scaled up many times over within a few minutes. This is called Infrastructure as a Service, or IaaS for short.
If the StartUp company uses IaaS service, it still needs to install the operating system, install the database system and set up a development environment. If these services are also offered by a cloud computing service provider, this is called Platform as a Service, or PaaS for short.
And finally: If we - as end users - use applications such as iTunes, Spotify, Office365 or GoogleDrive, then we speak of software as a service, or SaaS for short.