PCF is a commercial cloud platform (product) built by Pivotal on top of open source Cloud Foundry. PCF can be deployed on AWS, GCP, OpenStack, VMware vSphere, and some other IaaS platforms.
You should consider using PCF if you want to run your own cloud platform and you don't want to start from scratch.
When using PCF, you can deploy, configure and operate other products provided by Pivotal and their partners, or build your own ones based on your needs.
A typical use case for PCF is when companies want to deploy their applications on-premises for any reason (cost efficiency, flexibility, legal regulations, control over infrastructure, etc.). In this case they decide to use PCF as a leverage to build and operate their own (private) cloud offering. Another use case is when companies don't want to depend on the underlaying IaaS infrastructure. In this scenario, they rely on the fact PCF is IaaS agnostic to give them the ability to migrate if they need to.