Infrastructure as a Service (IaaS) – servers, storage, network and operating systems – as an on-demand service. Rather than purchasing servers, software, datacenter space or network equipment, clients instead buy those resources as a fully outsourced service on demand.
Platform as A Service (PaaS ) can be defined as a computing platform that allows the creation of web applications or software quickly and easily and without the complexity of buying and maintaining the software and infrastructure underneath it.
Software as a Service (SaaS) is software that is deployed over the internet. In a SaaS you are provided access to application services installed at a server. You don’t have to worry about installation, maintenance or coding of that software. An obvious example of SaaS is Microsoft’s Office 365, where the applications run remote from the user’s computer.
Watch this video. I like his style of explanation: