http://www.rackspace.com/knowledge_center/whitepaper/understanding-the-cloud-computing-stack-saas-paas-iaas
In simple terms:
SaaS (Software as a Service) applications are designed for end-users, delivered over the web
PaaS (Platform as a Service) is the set of tools and services designed to make coding and deploying those applications quick and efficient
IaaS (Instrastructure as a Service) is the hardware and software that powers it all – servers, storage, networks, operating systems