Something you probably noticed during the introduction to the CloudBees platform is that you never interacted with a human to get resources provisioned or tools setup. Everything is automated and managed by APIs, therefore, full-platform automation, such as ClickStart, is possible.
Creating new resources on demand, like we did by creating an application and database on RUN@cloud, is possible—thanks to Cloud elasticity—and relies on the mostly unlimited resources that IaaS has to offer.
As compared to self-managed infrastructure built on an IaaS, the main benefit of a PaaS is the time you save by not handling low-level stuff. Your engineering team probably could set up a Tomcat server on an EC2 instance as well as a Git server on a Jenkins instance. They even can have this scripted some way, so this can be quickly set up.
But this is only the emerged part of the PaaS iceberg, and does not even considering the time spent to set up such an infrastructure...