PaaS (platform as a service) occupies an interesting niche in the cloud ecosystem. It typically sits on top of IaaS (infrastructure as a service), which provides the ability to access remote computing resources. With IaaS you have machines, or virtual machines, that are not on your premises, that you can use as you wish. An example of IaaS would be Amazon EC2.
PaaS includes infrastructure, storage, database, information, and process as a service. Think of PaaS as providing remote computers, disks, databases, information streams, and business processes or meta-applications, all tied up in one "stack" or "sandbox." The applications may well be SaaS (software as a service), such as a CMS (content management system) or CRM (customer relationships management) system. Where a PaaS adds value over IaaS is to automate all the provisioning of resources and applications, which can be a huge time-saver.