On-prem means on-premise. When you have a server, you can either have it "on your own premise," meaning the server is physically located in the office, or you can have it so-called in the cloud, which means an external datacenter.
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The mesh is a collection of nodes, a lighthouse, and an admin center. The user device is a node, a server is a node, cloud stack is a node, LAN access box is a node.