Platform As A Service. Heroku & Amazon Web Services are both examples. In fact, they're nested examples!
Actually, AWS is generally categorized as Infrastructure-as-a-Service--although it's added a number of higher-level services that are more PaaS-like. (EC2 and S3 are definitely IaaS level. Elastic Beanstalk is pretty much a PaaS. Other services are in-between.)
PaaS is shorthand for Platform as a Service. Microsoft Azure and Amazon E2C are both examples of PaaS.
A third service layer would be IaaS; Infrastructure as a Service.