On-Premise means that as a customer you run the Simplifier on your own servers. Whether this is a dedicated root server, a virtual machine in VM Ware or a cloud computing instance at a cloud provider like Amazon does not matter in this case.
You are responsible for the installation, operation, maintenance, updates of the Simplifier instance and guaranteed availability.
To learn how to deploy the Simplifier on-premises, look at the Checklist for onPremise installations.