SaaS: Software as a Service
It simply means running applications at public clouds. The user uses these apps via the Internet. These apps are maintained by the Service Provider. Some e.g., of Service Providers, are SalesForce, Microsoft(Office 365), Oracle, Google(Google Apps), etc.
Salesforce was the first company to transform the world of Saas, and from that point, other companies have seen potential in this market and launched their apps.
Iaas: Infrastructure as a Service
It provides an environment for developers to build applications that users can use. IaaS includes:-
Users create virtual machines (VMs) on demand.
From a library of VM images.
PaaS: Platform as a Service
This is somewhat similar to IaaS but the difference is:
Developers provide an application which the platform runs.
They don’t directly create VMs.
You would be thinking that PaaS is simple and that is why mostly used. But this is not true. IaaS is 10 times popular than PaaS. Developers want to have more control over the resources.