IaaS is on-demand access to cloud-hosted computing infrastructure - servers, storage capacity and networking resources - that customers can provision, configure and use in much the same way as they use on-premises hardware. The difference is that the cloud service provider hosts, manages and maintains the hardware and computing resources in its own data centers. IaaS customers use the hardware via an internet connection, and pay for that use on a subscription or pay-as-you-go basis.
PaaS provides a cloud-based platform for developing, running, managing applications.  The cloud services provider hosts, manages and maintains all the hardware and software included in the platform - servers (for development, testing and deployment), operating system (OS) software, storage, networking, databases, middleware, runtimes, frameworks, development tools - as well as related services for security, operating system and software upgrades, backups and more.
SaaS (sometimes called cloud application services) is cloud-hosted, ready-to-use application software. Users pay a monthly or annual fee to use a complete application from within a web browser, desktop client or mobile app. The application and all of the infrastructure required to deliver it - servers, storage, networking, middleware, application software, data storage - are hosted and managed by the SaaS vendor.
