An on-premise PBX is exactly what the name entails. A PBX that is installed on-premise, i.e. physically in your office building. On-premise PBXs are deployed on servers that belong to the business and are managed by the business itself. Therefore, any business choosing to use an on-premise PBX should first ensure that they have the required infrastructure in place, such as servers, network, devices etc.
On-premise PBXs are better suited for large organizations which have the infrastructure, resources and know-how to configure and manage internally.